The broad Bayfront Drive sweeps gracefully around Sarasota Bay for almost a mile, circling one of the most beautiful waterfronts of any city in Florida.

You look out on a mammoth marina and take in a wide landscaped area that curves along the bay and ends in a huge botanical garden. Just across the bay are the keys -- long, narrow islands linked to the mainland by causeways and bridges. Beyond them is the Gulf of Mexico.

The first-time visitor who has battled US-41 traffic through Bradenton and the north end of Sarasota is hardly prepared for this peaceful postcard scene.

Sarasota, a city of more than 50000 some 50 miles south of Tampa, long has considered itself the "cultural center" of Florida. Artists, writers and artisans make this and the surrounding keys their home. Art galleries flourish, home and garden shows are frequent. There are concerts and theater productions for entertainment and museums to visit.

This is resort country, too, and "snowbirds" from the North fill hotels, motels and concominiums each winter. Golf courses are scattered around the city and probably no area has more shuffleboards than Sarasota.

Near downtown is a 28-acre Civic Recreation Center, with an auditorium, art association, library, community house, tennis and shuffleboard courts -- even lawn bowling.

There's boating and fishing, along with sightseeing cruises. And the beaches on the keys offer swimming and shelling. Water ski shows are presented free every Sunday afternoon from January through March, and the Chicago White Sox arrive in February for their spring training.

On the way in on Us-41, the tourists passes the Ringling Museums and Van Wezel Performing Arts Hall, two of the most popular spots in town. The gardens at the south end of Bayfront Drive are the Marie Selby Botanical Gardens, acres of colorful plants and foliage, plus an exceptional greenhouse. g

Prime movers in establishing Sarasota as a cultural center were John Ringling of circus fame and his wife, Mabel. The Ringling Museum of Art will celebrate its 50th anniversary this month. It opened in 1929, but the museum complex now includes the 30-room Ringling home, the 18th-century Italian Asolo Theatre and the Museum of The Circus.

Ringling built the art museum as a gift to the people of Florida, and it contains one of the most comprehensive collections of baroque art in the United States, including a group of works by Peter Paul Rebens. Paintings and numerous pieces of statuary were selected by Ringling himself as he toured Europe seeking circus performers.

Last year, the museum underwent renovations that changed its whole appearance. Drap wallpapper was removed from the galleries, walls were painted a gleaming white, and a new track lighting system was installed. Paintings also have been rearranged chronologically so that one may easily follow the history of Renaissance and baroque painting. The New Wing Gallery, opened in 1967, exhibits the museum's growing collection of contemporary art.

The Ringling home nearby, built with a wide veranda on Sarasota Bay, is called Ca'd Zon, "House of John" in Italian dialect. Modeled after the Doge Palace in Venice, it was constructed in 1925-26 at a cost of $1.5 million.

The windows are of tinted Venetian glass, roof tile were imported from Barcelona, the great hall has a checkered floor of black squares of marble from Belgium and white squares from Alabama. Much of the elaborate furniture came from the estates of Jay Gould and Vincent Astor, and the crystal chandeliers came from the original Waldorf-Astoria Hotel. Art objects are from all around the world.

When Ringling died in 1936, seven years after his wife, he gave his entire 68-acre waterfront estate to the State of Florida. In 1948, the state established the Ringling Museum of The Circus as a tribute to Ringling and his accomplishments. It houses a collection of memorabilia from the Big Top and those who performed under it. Winter quarters for the circus were in Sarasota for years, but a decade ago moved to Venice, 15 miles south. However, performers and buffs drawn by the Ringling family's long personal association with the circus still live here.

The Asolo Theater was built in 1798 in honor of Queen Catherine Conrro of Cypress, who had been dethroned and exiled to the little town of Asolo near Venice. In 1930, the playhouse was dismantled to make way for a movie theater, purchased by a Venetian antique dealer and stored away for 20 years.

The state purchased it in 1950 and reassembled it here in an air-conditioned building built especially for that purpose. The theater presents a full program of winter operas, a 10-play repertory of modern and classical plays and a year-round schedule of arts films, lectures, concerts and recitals.

The Van Wezel Performing Arts Hall, a bright purple shell perched on the edge of Sarasota Bay, opened just 10 years ago. It was designed by Frank Lloyd Wright's Talissen firm and the color was designated by Mrs. Wright. It has been called everything from the "Purple Cow" to the "Purple People Seater" but has been a huge success.

The hall's programs, ranging from ballet and opera to musical comedies and jazz concerts, from Beverly Sills to Count Basie, have proved so popular that more than $200000 in ticket orders had to be refunded to persons on the mailing list seeking reservations for the 1979-1980 season. The hall, unfortunately, seats only 1,778.

No trip to Sarasota is complete without a visit to the keys -- St. Armand's, Longboat, Lido and Siesta.

Ringling in the 1920s purchased St. Armand's Key just across the Ringling Causeway and laid out the shopping circle that since has become famous, with some 100 shops, boutiques, galleries and restaurants.

Just west of St. Armand's is Lido Key with a string of resort hotels and motels and a half-mile-long white sandy beach. In the other direction is Longboat Key, with more resorts along with condominiums, private homes, marinas and restaurants. Siesta Key, with two connections to the mainland has its share of motels and concominiums, but also has scores of private homes hidden in groves of pepper trees, mangroves, palms and pines.