IT IS possible, when the sun sets in Miami, dripping Crayola purple and orange along the horizon, to suspect just how beautiful and wild South Florida was 20 years ago -- before the people began to arrive, to pave and subdivide and maul the land.

Miami has gotten a reputation in the last three years for being wild in a different and much less attractive sense. Largely because of media attention focusing on South Florida's drug and immigration problems, people in the rest of the country don't think of Miami as the vacation idyll they once did; they think of it as a place where you're as likely to get murdered as to get suntanned.

That impression, reinforced by last November's Time magazine cover story which showed a map of Florida with the headline "Paradise Lost?" burned across the state's southern tip, is wildly out of line with reality. South Florida is still one of the best places in the country to be, to vacation or live.

If you go to the part of the Everglades where the tourists do not go, you can stand on a dirt road and look out forever on what appears to be an undifferentiated plane of saw grass. The sky is a huge dome, the silence is as big as the sky and the swamp together, and nothing seems to be moving. And then -- just like that moment in an optical illusion when you suddenly see what you've been missing all along -- the swamp jumps to life and everywhere you look alligators, garfish , herons, ducks, spoonbills, dragonflies and mosquitoes are conducting all sorts of fascinating business with each other.

This place is the Shark Valley of the Everglades, and you get to it by going west on U.S. 41, the Tamiami Trail. At the northern edge of the Everglades, it is in an area where the wildlife is more wild, more interesting, and less accustomed to being gawked at than the wildlife in the Florida City part of the Everlades, south of Miami on U.S. 1.

The violence in South Florida that has been given so much national media attention is far from random. The people who get machine-gunned to death, who get tossed from the tops of buildings, who float to the surface of Biscayne Bay, all know each other. They're all tied into South Florida's drug culture, and they are killing and robbing each other.

And although even Florida's governor admits that illegal drug importation is Florida's major industry (outdistancing tourism), no one takes the time to point out that the South Florida drug scene is a wholesale one, not a retail one. Which means there aren't large colonies of addicts waiting to rob innocent tourists to support drug habits. South Florida's drug culture is populated by people who dress very nicely.

So, despite publicity to the contrary, the visitor to South Florida has a lot less to worry about in terms of crime than, say, the average visitor to New York City. Unless he or she is in Miami on "business."

South of the city of Miami, where Interstate 95 inauspiciously begins its cross-country journey, is Alice B. Wainwright Park, a small and quiet and beautifulplace that very few people know about. It looks out over Biscayne Bay. It is a marvelous place to lie and read the Sunday newspaper: carpeted with pine needles, amazingly isolated from the city which surrounds it, with a view from which one can watch the bay's daily cycle. The heat doesn't seem to get into Wainwright Park, what with the roof of trees and the sea breeze, and you can always go for a dip. You're likely to be alone.

Miami is undergoing a gawky adolescence. Fifty years ago, going to Miami was like going to the edge of the frontier. Where most of the metro area is now, there was nothing but swamp. Even 15 years ago Miami and its suburbs were sleepy towns.

These days, the country just to the north of Miami is one of the fastest growing regions in the nation. In downtown Miami, where for 10 years the tallest building had no more than 45 floors, eight skyscrapers taller than 50 stories, some well into the sixties, are going up. The entire skyline is being transformed.

The growth has meant problems, heaps of problems for which Miami hasn't really had the political talent to deal imaginatively and effectively. But Miami is very young as a metropolitan area. It didn't have the 200-year head start that New York and Boston had.

There is a lot of kitsch on the tourist path in South Florida. You can see parrots ride bicycles across high wires, see men feed sharks, see Flipper (in four or five different places), and go shopping in endless air-conditioned malls which seem to spring from the ground like mushrooms after a summer rain.

But you don't have to go to the places all the other tourists go. And, in fact, the soul and spirit of Miami are much better captured in the places the natives go to amuse themselves.

There is, for instance, Coral Castle. Twenty miles south of the city proper, right on U.S. 1, there is a home built by a Latvian immigrant named Ed Leedskalnin. The home is carved completely out of the coral rock of which Florida is composed. A rock gate weighing thousands of pounds is so delicately balanced that it swings open with only slight pressure. A several-ton crescent moon is perched high on one corner of the home's open-roofed walls. The furniture is carved from coral, and is surprisingly cool and comfortable.

Coral Castle is a minor mystery of the pyramid sort. As the guides will tell you, between 1920 and 1930 Leedskalnin carved the home entirely by himself. The mystery is that he managed to maneuver the massive objects he carved into their positions; and that then in 1930, when Leedskalnin had completed it, he walked across U.S. 1 and laid his head down on the railroad tracks to die.

When heading south by car out of the city of Miami, there are two choices. You can drive along U.S. 1, the commercial strip alongside which Miami's new monorail-like mass transit system is taking shape. Or, you can cut to the east, off U.S. 1, at Vizcaya and take Main Highway and Old Cutler Road south. The drive along Main Highway and Old Cutler is infinitely more interesting.

The road winds through the old bayside residential district south of the city. It passes through Coconut Grove, Miami's equivalent of Greenwich Village in the '60s that now has pricey boutiques and artsy film theaters and clings to a vestige of its counterculture past. But the drive becomes beautiful just beyond Coconut Grove, when Old Cutler Road leaves the city completely behind and moves, beneath a complete canopy of overhanging trees, through residential neighborhoods. Especially during the day, Old Cutler is a cool, beautiful, green tunnel. The drive is well worth the time even if you only turn around after a while and head back north. (To get anywhere, you'll eventually have to cut back west to U.S. 1.)

All the beaches in Miami are equally crowded on the weekends and holidays, but they are not all equally beautiful. The best beach, the beach the natives use, is really no farther out of the way than the other beaches. It's just that very few people ever get to it, because you have to drive past most of the other beaches to reach it.

About 10 minutes beyond Key Biscayne's Crandon Park Beach, behind Richard Nixon's favorite Florida restaurant, The Jamaica Inn, is Bill Bagg's Cape Florida State Park. It occupies the southernmost tip of Key Biscayne, well south of the hotels and the more popular beaches. It is the beach to go to. It even has an old lighthouse, which has been restored and is open for tours. From the top of it, you can see much of South Miami.

Miami is very flat. And the sky over Miami is clear and blue and much grander than the sky almost anywhere else in the United States.

The sky is so huge because the land is so flat. And the sky, perhaps in repayment for the flatness, puts on a continual show for the land. South Florida boasts some of the most beautiful and most interesting clouds of any region in the country. There are enormous, threatening, absolutely black thunderheads, there are lines of squalls, there are small puffy cottonballs. And the weather is such that in the Everglades or at the beach, you can lie on your back for 15 minutes and watch the clouds form and take shape and move out, as in a time-lapse movie. The procession is magnificent. Much more impressive than the Orange Bowl parade.

On the Sunday in May 1980 when rioting erupted in downtown Miami, a full-page color ad ran in the New York Times Sunday Magazine, placed by Miami's tourist authority. It depicted two beautiful, white, upper-middle-class adults, a man and a woman, lying in a hammock facing each other, laughing, and feeding each other bagels and lox. Spread out on a table before the hammock was a sumptuous brunch. The ad's copy line: "Miami -- See it Like a Native."

The irony was cheap, and has been frequently exploited -- to good effect -- by Miami's political cartoonists. And that ad campaign is a thing of the past, given South Florida's recent history.

But the idea behind the ad was fine and true indeed. Miami is as marvelous as it ever was. You just have to look a little harder to see it.