CHICAGO Mayor Jane Byrne looked quizzically at her aides. It was last summer, and Hollywood producer John Landis was in her office to discuss the filming of "The Blues Brothers." He had just told the mayor that things were going well, except for one hitch:

Landis had been unable to get permission for a key scene in which the car was to crash through plate-glass windows of Chicago's Daley Plazza, the city hall complex named for her predecessor.

The city has strictures against motorized vehicles on public walkways and in public buildings, but a mayoral spokesman said no one at the meeting had a good reason to explain "why the necessary waivers could not be obtained."

"Do it," Mayor Byrne commanded.

The scene was shot as planned, and the Dan Aykroyd-john Belushi movie is now playing around the nation.

Byrne's gesture was dramatic -- but not unusual. In the past 10 years, nearly every state and more than a dozen cities have set up special agencies whose role is to lure moviemakers out of Southern California, promising them ease in filming, new and varied shooting locations and lower filming costs.

"The reason is the same all over: the economic benefit," said Phil Cole of the Alabama Film Commission.

The stakes are high.No nationwide figures are available for the amount of money spent on motion pictures every year. But a recent University of California at Los Angeles study -- probably the most comprehensive academic look at the economic effects of film production -- estimated that, because of the "multiplier effect," the $1.05 billion spent on filming in California alone in 1979 had a total impact of $3.8 billion spent on the state's economy.

New York City's Office of Motion Pictures and Television estimates that feature films pumped $238 million into the city's economy last year and that other filming -- from soap operas to industrial films -- contributed another $262 million.

"It's a marvelous way to bring in new dollars with a minimum investment by the state and virtually no investment by the taxpayers," according to Lucy Salenger, who heads the Illinois Film Office. Typically, a state or city motion-picture office has a budget in the hundreds of thousands of dollars. But one film can deposit five or 10 times that amount in a several-week shooting schedule.

Cast and crews must be fed and housed. Laborers must be hired. Lumber must be purchased. Extras collect their pay. Equipment has to be rented. In bigger cities like Chicago and New York, local studios, technicians and even actors are hired on location.

Walter Coblenz, who is filming "The Legend of the Lone Ranger" near Santa Fe, estimates that by the time he leaves the production will have deposited $5 million in New Mexico.

Tiny Lima, Ohio, was enriched by about $750,000 because the ABC television film "Attica" was made there, producer Lou Rudolph said.

Economists say the ultimate economic impact is far greater than the direct expenditure by a production company. Not only do cast and crew members, like tourists, visit dry cleaners, cocktail lounges and theaters, but local merchants and workers spend more because of their augmented earnings. Goodbye Hollywood?

According to Michael Linden of the Motion Picture Associating of America, preliminary statistics show that the number of feature films made entirely in California jumped form 57 in 1978 to 69 last year, while the number of films shot both in California and other states was 26 in both years.

The number of films shot entirely outside however, increased sharply. In 1978, 55 films were made outside Hollywood (but in the United States), while last year 77 movies were made in states other than California.

In 1975 California set up its own Motion Picture Council as a defensive move to keep moviemakers from leaving the state. Chloe Pollock, who heads the California office, said that california is a large state "and there are many areas that are not as well known to filmmakers as others are."

State film commissions cannot, or at least do not, offer subsidies to moviemakers as many European or Latin American countries do.

Nor, because of their stringent budgets, do officials spend a lot of time on the West Coast cozying up to producers -- although many do take occasional trips, and New York Gov. Hugh Carey accompanied his new film-office director Thea sklover to Hollywood last November to extol New York's virtues.

State and city film commissions know how to find what moviemakers need -- whether it's flowering vegetables in midwinter or a piece of equipment in the middle of the desert. They keep extensive files of every potential shooting location in their jurisdictions. Some states and cities have direct liaisons with police departments and other agencies to handle the technical problems involved in shutting down an expressway for a "chase" scene or re-routing an elevated train for a shot. Lowering the River

The made-for-television film "centennial," shot in Ohio a few years ago, needed a river for stars Greg Harrison and Stephanie Zimbalist to ford as they plodded off into the wilderness in a Conestoga wagon.

The Ohio Film Bureau found the river and the virgin woods necessary to simulate wilderness and negotiated with the farmers so that the company could build the roads embankments necessary.

But when the four-ton Conestoga, pulled by six tons of Percheron horses, hit the river's edge, animal handlers vetoed the crossing, saying the river was too swollen with spring rains for the horses and cast to ford safely.

"So we found a way to lower the river, a tributary of the Tuscarawas," said Mary Barnum, who heads the Ohio bureau. Barnum's aides found a dam upstream on the main river. Because of the recent rains, the irrigation needs of the farmers were not critical, and conservation authorities agreed to close the dam to reduce the flow through the tributary.

Movie-makers, however, are more likely to find themselves tilting with stale locations or local bureaucrats than with Mother Nature.

"The most important thing film bureaus can do is prepare extensive brochures showing me everything that is abailable in the state," the "Lone Ranger's" Coblenz said.

Although the movie is set in Texas -- and Coblenz began his location search in that state -- he chose New Mexico because four of the five locations he needed -- from a deep ravine to flat terrain where he could build a town to giant boulders for an ambush scene. Texas, the purported locale of the movie, "did not have the kind of look we needed," he said.

Sometimes, even when the needed look is there, the location is unavailable.

Rudolph, whose re-creation of the famous New York prison riot aired on ABC in March, said he knew that the prison-yard scenes could not be shot within the maximum-security penitentiary, although he was able to film two days in front of the prison. Rudolph's staff sent letters to prison facilities and film bureaus across the country. He found a startling likeness to the Attica prison yard in Lima, Ohio, at the state hospital for the criminally insane.

The Ohio bureau did not have to lower rivers for Rudolph, but it did have to coordinate the filming of a prison riot -- with as many as 700 persons on the set -- while 400 patients continued to be treated at the facility.

The crew did have to cope with one attempted breakout. Five extras were mistaken for patients and an actor ended up in a locked ward for a while. Generally, however, the filming went smoothly.

The Ohio bureau assigned a staffer full-time to coordinate the needs of the hospital with those of the movie company and also joined with the state's employment service to screen and process thousands of extras. Competing for the Cameras

While film bureau officials, such as New Mexico's Larry Cortez Hamm, argue that movies can be made more cheaply outside Hollywood, most producers say cost is not much of a factor in their decisions.

"On location we have to house and feed the crew and cast. Although local labor is cheaper, it is not as experienced as that in Los Angeles. We leave Los Angeles for one reason -- the setting," Coblenz said.

Clearly, however, producers may leav e in search of authenticity, but verisimilitude often will suffice. And film-bureau directors have become experts at describing how their states can be made to look like other states.

"We can simulate anything but desert states or high mountain glacier states," contends Alabama's Phil Cole. "We've got prairies, flatlands, tropical areas and big cities. You can roll over a hill and if we take off the Tv antennas and put up a few Coke signs, it'll be Maybnerry RFD on practically every corner."

The District of Columbia is making a similar pitch. "We're trying to convince filmmakers that we're more than must malls and monuments," said Richard Maulsby, director of the District of Columbia's newly established Office of Motion Picture Development.

Once a film company comes to Washington to get shots of the landmarks, "it makes sense to stay. D.C. is more than just a nation's capital. It's an international city with varied neighborhoods.Parts can be made to look like New Orleans, or Boston, or Philadelphia."

But Washington is fighting more than its image as a place to shoot the monuments and leave. It is fighting a reputation as a terrible place to make movies, despite the city's reservoir of technical expertise.

"I'd go to a lot of places, but I wouldn't go back to D.C." said Coblenz, who produced "All the President's Men" in 1975. "It's a good setting for a motion picture," but nearly impossible to shoot in because of the jumble of jurisdictions: the District government, the federal government, the White House, Capitol Hill and the U.S. Park Service.

But Maulsby said his new office will end all the confusion. "We're basically a one-stop office for all the permits. D.C. is a decent place to shoot films now."

"Maybe it will be easier to film there now," Coblenz conceded.

Since the D.C. office opened last September, parts of four feature films have been shot in Washington, down from six the previous year, Maulsby said. But recently there has been a slight upsurge of interest. Maulsby said he has been in contact with 18 feature films in recent months and four are scheduled to shoot in the nations's capital between August and November, although that could change with script revisions.

During the last nine months, moviemakers (including those shooting commercials and documentaries) left $1.2 million in Washington, about the same as in the nine months before, Maulsby said.

Like Washington, New York City, with its welter of restrictive union rules, crowded streets and high prices, has not been a traditional favorite of moviemakers. But they never abandoned the city because "you can't duplicate New York," said Coblenz -- although the quintessentially Manhatten film "Looking for Mr. Goodbar" was filmed in Chicago.

But in recent years, New York City has made a concerted effort to remove the difficulties of shooting there. Unions whose contracts were adapted to the needs and hours of the stage have adopted a flexible attitude toward the requirements of motion-picture producers. The city has taken steps to fill the studio and soundstage needs of producers. (It reactivated a Queens soundstage due to be converted into a gymnasium to keep Woody Allen from being forced to shoot elsewhere, Sklover said.)