The seaside resort city of Long Beach has had some rough times. It has grown older and more urban and some years ago lost the Miss Universe Pageant. But California Gov. George Deukmejian lives there now and four Olympic events including archery are scheduled for the city, which could experience a rebirth of its tourist heyday.

The archers will use El Dorado Park, just north of the San Diego Freeway. Its existing 250-meter wide range can accommodate 50 targets, the only site of its kind in southern California. Sea breezes make Long Beach's summer air cool and clean, compared to the sun-baked, hazy brown atmosphere of the coliseum 20 miles inland. Temporary grandstands at the park will seat roughly 4,000. ATHLETICS

(Track and Field)--The Los Angeles Memorial Coliseum was completed in 1923 for the breathtaking sum of $954,872.98. The organizing committee and the Atlantic Richfield Corp. will spend $5 million this year simply to install an eight-lane, all-weather track, plus running, jump and pole vault lanes, javelin runway, high jump pit and other frills. ARCO is also building six other all-weather tracks at schools throughout the area.

Nothing will be done to the giant Olympic torch that sits 150 feet above ground level on the peristyle at the stadium's east end. It reminds all that the last Summer Olympics in the United States were held there in 1932, making the coliseum the only stadium in the world ever to host two separate Olympics. In honor of the occasion, Olympic committee spokesman Bill Schulz said, the beer advertisements painted on the peristyle for football fans will be removed. But advertisers will spend $12 million for two huge electronic scoreboards and a video screen, with the understanding they can display promotions before and after the Summer Games.

Los Angeles officials increased the coliseum's seating from 75,000 to 101,574 just before the 1932 Games so they could call it the largest stadium in the world. Conversion to modern theater-type stadium seating has reduced capacity to 92,604, with 74,017 permanent chairs and 18,587 of the old bench seats.

The 1984 Olympics will hold the opening ceremonies there, with each of the competing teams marching in through the peristyle and down a ramp built over the east end zone seats, and President Reagan is scheduled to welcome the Games from a stage under the peristyle. The Olympics will also end here, with the finish of the marathon run. The marathoners will begin in the fashionable coastside town of Santa Monica, home of Jane Fonda and thousands of other personal hygiene enthusiasts. After taking a roundabout course through the city's still existing surface streets, they will finally burst into the coliseum, the home of thousands of beer-guzzling Raiders and USC fans. BASEBALL

Dodger Stadium is the brilliant jewel at the peak of southern California's athletic crown. Seen as one approaches it for a night game, as are almost all baseball games there, it glows softly amid scattered palms on a high canyon above downtown Los Angeles. The stadium is kept unusually clean and parking is easy to find, if difficult to retreat from. In 1982 the Dodgers set the major league attendance record--3,608,881--an average of 44,554 a game in the 56,000-capacity stadium.

There will be no Fernando Valenzuela to lure Dodger faithful during the 1984 Olympic baseball tournament, but the novelty of the event should draw good crowds. Baseball, like tennis, will be a "demonstration" sport at the Games. The United States and five other teams will compete--one from Asia, one from Latin America, one from Europe and two more to be decided. For the U.S. team, only amateurs need apply. BASKETBALL

A smile lit the face of Boris Stankovic, the Soviet who serves as secretary-general of the International Federation for Basketball, when he stepped into the cavernous Forum in Inglewood two years ago. There were 17,505 seats, with an enormous multifaced scoreboard hovering over the court for Los Angeles Lakers pro basketball games. There those most revered capitalists, Kareem Abdul-Jabbar and Magic Johnson, strutted their stuff. There an American corporation, in its own tentative way, even promoted a hockey team, an enterprise dear to any Russian.

Comrade Stankovic was impressed: "We are very honored to have the basketball tournament in a place such as The Forum." BOXING

Rocky Balboa's titanic struggles against Apollo Creed in "Rocky" and "Rocky II" were supposed to take place in Philadelphia, but that was the Los Angeles Memorial Sports Arena we saw on the screen. If that does not impress the Olympic boxers who will gather there, guides may point out that the arena was dedicated on the Fourth of July, 1959, by then-vice president Richard M. Nixon, himself no stranger to comebacks.

The arena seats 16,353. Its all-time attendance record for boxing is 16,230, who gathered in 1962 to see a young hero of the 1960 Olympics, then known as Cassius Clay, knock out the aged Archie Moore in four rounds. CANOEING/ROWING

About 10,000 spectators will have seats on the shores of Lake Casitas in northern Ventura County for the boat events. This reservoir, created in 1959, sits amid a classic California landscape of live oaks and yellow-brown grasses. It attracts campers and fishermen; waterskiing is banned.

The Olympic organizing committee has arranged to repave roads to the lake in lieu of fee for its use. It will provide contestants in the strenuous races an atmosphere free of smog and far from the hurly-burly of the other Olympic events. Olympic officials said this is the first time since the rowing and canoeing events were held on Italy's Lake Albano that rowers will use an existing lake not specifically constructed for boat races. CYCLING

A foreign visitor approaching Cal State Dominguez Hills, site of the brand new Olympic Velodrome, may rejoice to see southern California just the way it is often described abroad. In the raw and rapidly growing community at the confluence of the San Diego, Artesia and Harbor freeways, huge stork-like oil pumps bob up and down in the middle of the Colony Cove Mobile Estates--acres of trailer homes. Carls Jr. occupies one corner; a new Baskin-Robbins is going in at another corner. Across the street from the campus huge signs advertise townhouses for $92,500 and up, models ready for inspection.

At the western end of the university, constructed in an isolated spot amid weed-strewn vacant lots, is the new velodrome, or cycling track. The $3 million facility is the only world class, certified cycling track in the western United States.

The smooth concrete surface slants at a terrifying 33 degree angle at either end, to accommodate cyclists whirling about at 40 miles an hour with no tread on their tires and no brakes. The Southland Corporation, which runs 7-11 stores, provided the money for the facility. Although many velodromes are indoors, officials here decided that was unnecessary in California and far too expensive. The indoor velodrome for the Montreal Games cost $56 million.

The velodrome will revert to full use by the university after the Games. University space and facilities associate Ken Schwartz said the track has already begun to attract cycling buffs on evenings and weekends, although Dominguez Hills students still seem to prefer cross country cycling. The scenery is a bit more varied that way. EQUESTRIAN

Post columnist Andrew Beyer noted during his recent sojourn at Santa Anita Park in Arcadia how horses sometimes appeared to stop short when overcome by thick San Gabriel Valley smog. But Olympics officials feel the equestrian events will do quite nicely there.

Santa Anita has stable accommodations for about 350 horses, but more importantly can provide parking for 22,000 automobiles. Next to the race track sits the huge Fashion Park Shopping Mall, a fine place for foreign visitors to stroll after the events and see the ultimate in American consumer technology. FENCING/VOLLEYBALL

The Long Beach Convention Center Complex, with its circular arena dominating the landscape, rests at the end of one of California's longest and broadest beaches. It provides an excellent target for joggers running into the sunset. Fencers, alien beings to most Long Beach residents, will use the 100,000 square foot exhibition hall of the convention center, which will seat 6,000 spectators.

Volleyball, a southern California passion, will be played in the Long Beach Sports Arena, which seats 11,329. FOOTBALL (SOCCER)

The Rose Bowl was completed in 1922 for only $272,000, part of the early 1920s building spree that also produced the coliseum. Anyone who witnessed the Redskins' victory there in January knows the simple, architectural magic of this park, where even those in the last rows of the 104,696 capacity seating somehow feel close to the action. Those Redskins fans also know the horror of driving into or out of stadium parking lots, wedged into a Pasadena canyon with few outlets.

Although cycling events were held there in the 1932 Olympic Games, the Rose Bowl was always meant for American football. UCLA plays its home games there now. The stadium has, however, hosted 45 professional soccer games, mostly from 1978 to 1980 when the Los Angeles Aztecs used it as a home field. Each Saturday, the huge grass field south of the stadium is full of children in brightly colored uniforms of the American Youth Soccer Organization, all dreaming of some day taking America into the World Cup.

Europeans, particularly those from the United Kingdom, leaving the Olympic soccer matches here will be stunned to find congenial resting spots in those run down parts of downtown Pasadena that have not yet been redeveloped. A few English-style pubs have mysteriously sprung up, bearing names like the Loch Ness Monster. GYMNASTICS

Pauley Pavilion has left its mark as the home of the UCLA basketball team, the pit full of noise and NCAA championship banners where Lew Alcindor (later Kareem Abdul-Jabbar) and Bill Walton performed many wonders. But it has a quieter side. The UCLA Gymnastic Classic is held annually in the $5 million facility. For the Olympic gymnastic competition, the stadium will provide permanent seating for 10,337 and collapsible floor-level bleachers for another 2,376. HANDBALL

Olympic officials had promised two separate gymnasiums for the handball competition. But ABC Television discovered it could not send a clear signal from the remote campus of Cal Polytechnic-Pomona, and the International Handball Federation balked at having a competition split in two. The competitions will now be confined to one 4,000-seat gym, at Cal State-Fullerton. FIELD HOCKEY

The East Los Angeles College Stadium rarely entertains even a local television camera crew, much less a full-blown international sports event. But then field hockey remains on the fringes of the Olympic program, and is of even less interest to southern Californians.

The college stadium sits near the border of East Los Angeles and Monterey Park, part of the cosmopolitan, industrialized flatlands east of downtown Los Angeles where many Latinos and Asians live. The whole area has a suitably international flavor, with small restaurants for every imaginable cuisine. The stadium seats 22,000, has good parking and may be a perfect spot for those who wish to sample a quieter Olympics, beyond the full glare of television. JUDO

That same connoisseur of the Olympics' quieter, more exotic edges need only take a pleasant two mile stroll north from East Los Angeles College, or drive a couple of exits up the Long Beach Freeway, to reach Cal State-Los Angeles. This 4,200 seat facility seems ideal for the Olympic judo competition. It has already hosted the U.S. national championships, bowing to the interests of its neighbors of Asian descent and of legions of martial arts devotees in California. MODERN PENTATHLON

The resort of Coto De Caza thrives on eclectic American athletic passions. Accordingly, it will host the crazy-quilt modern pentathlon, a combination of horseback riding, fencing, pistol shooting, swimming, and cross country running.

This 5,000-acre facility has about 600 affluent residents, plus hotel space for occasional visitors. They may dabble in swimming, volleyball, basketball, bowling, horseback riding, quail hunting, skeet and trap shooting, or pile into the community's star attraction--the Vic Braden Tennis College. SWIMMING/DIVING

Workmen have laid down the black tiles marking lanes at the bottom of the new 50-meter outdoor swimming pool at Southern Cal, not far from the coliseum. The huge, multi-level platform arching over the accompanying diving pool already has "USC" artistically embossed in its concrete base. Despite construction slowdowns because of rain, the facilities should be ready in June and will be turned over to the university after the Olympics.

The McDonald's Corporation, beholding to the considerable appetites of USC undergraduates, has committed $4 million to build the swimming and diving facilities. Huge temporary bleachers will allow 11,000 spectators to watch the action. But just as good a view can be had from the top deck of a nearby parking lot TENNIS

UCLA is the tentative site for this demonstration sport. Tennis was an official Olympic event until after 1924 and will become one again at the Seoul Olympics in 1988. Sixteen men and 16 women will compete. Professionals will be eligible if they have not reached their 21st birthdays before competition ends. WATER POLO

Pepperdine University, perched on its lovely hillside campus overlooking Malibu, will host the water polo tournament. The Raleigh Runnels Memorial Pool has room for about 5,000 spectators. Pepperdine is no stranger to athletic greatness. Its basketball team has been nationally ranked, but more importantly the university has been the site of several recent episodes of the Battle of the Network Stars, Howard Cosell's Olympic warmup. WEIGHTLIFTING

The agonized grunts of fireplug-like Russians may be drowned out by the din from Los Angeles International Airport, just south of Loyola Marymount University where Olympic weightlifting will be held. Competitors will use the campus' new Albert Gersten Pavilion, which seats 4,500. Athletes may warm up and train in the university gym next door.

The Eastern bloc may have the best weightlifters, but the Olympic organizing committee here has selected a commissioner for the event sure to project the best of American spiritual and physical supremacy. He is Donn Moomaw, minister of the Bel Air Presbyterian Church where President Reagan once worshipped. Moomaw was an all-America lineman at UCLA and an all-pro in Canadian football three decades ago. He refused to play U.S. professional football because it insisted on having games on Sundays. WRESTLING

The 1984 Olympic wrestling competition may draw more than its usual share of foreign spectators. The long drive from downtown Los Angeles along the crowded Santa Ana Freeway can sometimes take more than an hour, but the Anaheim Convention Center, the wrestling competition site that is the driver's destination, is within sight of Disneyland. Anyone who tires of sweat and canvas in the 8,892-seat Convention Center arena may walk down the block for a Matterhorn ride. YACHTING

Long Beach captures both the beginning and the end of the Olympic alphabet. In other recent Olympics, the yachting competitions have been held far from other events, in places like Acapulco, Kingston and Tallinn. Next year they will be much closer to the center of things, at the Long Beach Marina and Harbor.

The city possesses one of southern California's best natural harbors, one more asset the Los Angeles Olympic Organizing Committee will not have to pay for. TICKETS

Olympic tickets will go on sale nationwide in early June, according to spokesman Amy Quinn. At that time, 32-page booklets will be available at local retail outlets to be announced; these booklets will include order forms and events schedules.

Random computer selection will determine who gets tickets for high-demand events; these order forms must be returned within 60 days after they go on sale. For the rest, it will be "first in, first served," Quinn said.

The average ticket price for one session (half-day) is $18, Quinn said, with 3,000,000 on sale for less than $10.