Palm Beach, Fla.

One of my pet indulgences while on the road is having breakfast in a sidewalk cafe - on a warm morning, of course, with palm trees waving nearby. On such a morning in Palm Beach, as I waited for my French toast and gazed around Testa's Restaurant - hard by a row of stately palms on Royal Poinciana Way - I realized that a good portion of the diners were suited up and on their way to work.

Why that should have surprised me is that until then I'd always assumed everyone in Palm Beach was on permanent holiday. Such is the feeling you get among the high privets and manicured croquet lawns of that venerable resort, which has been sheltering winter escapees for exactly 90 years. Palm Beach is the place that once tried to bar the Kennedys, but today there seems a loosening , a leavening of the old ways. You don't even need to wear sockless loafers or a green jacket - badges of Palm Beach status - to have a good time.

It was in 1894 that Henry M. Flagler, a pioneer Florida developer, having stretched his Florida & East Coast Railway to the sandy 14-mile-long island, opened the huge, rambling, yellow-frame Royal Poinciana hotel. The hotel is gone , but Whitehall, Flagler's 1900 mansion, has become a museum, depicting Palm Beach's turn-of-the-century character.

I passed beneath the blinding white pillars and through the portals of Whitehall one morning and in the period rooms and pictorial displays and learned , among other things, that Flagler was responsible for having brought golf to Florida (though competition from Cuba prevented him from starting a pineapple industry).

Old Palm Beach also owes much to Addison Mizner, the ''Aladdin of architects, '' who built many of the blocky stucco Italianate mansions along South Ocean Boulevard, on route A1A. Dodges, Wanamakers, and Vanderbilts made their winter homes here, but perhaps the most princely palace of all was Mar-a-lago, which Mizner built for Marjorie Merriweather Post. Most of the estate is hidden behind wall and hedge at 1100 South Ocean Boulevard, but one gets a hint of the opulence in the dazzling blue-stone Moorish gate in front.

Lake Worth, at a widening of the Intracoastal Waterway, separates Palm Beach from the less rarefied West Palm Beach. There I enjoyed an almost solitary tour of a gem of a museum, the Norton Gallery of Art. It is strong on French Impressionism, 19th- and 20th-century art, and Orientalia; a Gauguin, Pollock, Braque, and Chagall are among its most treasured pieces. Perhaps the most arresting work is a Duane Hanson sculpture of a worker in jeans and T-shirt lolling against a wall. Hanson lives in Dania, Fla., and the model for the sculpture is a resin salesman he knows, who makes occasional appearances at the gallery, confusing and amusing unsuspecting patrons.

Since the Royal Poinciana burned down, the leading old-line hostelry has been The Breakers, an Italianate palace by the sea that is topped with twin belvedere towers and surrounded by acres of fairways and croquet lawns. The Breakers is winter headquarters for Palm Beach society, site of annual balls and banquets. Even when it is sold out, as usually is the case in winter, the 568-room hotel has loads of uncluttered public space - inner courts with splashing fountains, colonnaded loggias. The guest rooms come with large walk-in closets, stocked with personal safes.

The Breakers is a throwback, an anachronism. How often do you find a hotel with poky elevators operated by hand, a tie and jacket requirement for men after 7 p.m., eating to string music in a huge vaulted dining room, or croquet on the front lawn?

There is even a croquet pro, E.T. (Teddy) Prentiss IV, who looks more like a linebacker and favors shorts over the traditional long whites.

There are more relaxed places to stay in Palm Beach, such as the Brazilian Court, on a quiet back street just off Worth Avenue, a three-block parade of swank shops, galleries, and restaurants. The 1920 white-stone hotel is a low-rise block that surrounds two lovely inner courtyards, one for lounging, the other for dining. Behind a tangle of tropical greenery lies a cloistered little swimming pool.

Eating out in Palm Beach is not the stuffy white-cloth affair one might expect, not at Chuck and Harold's or Charley's Crab or 264 (named for its address on South Ocean Boulevard), and certainly not at Testa's. That's where you'll see working people stopping for breakfast on the way to the office. It must make the workday go that much faster, knowing the manicured old resort is waiting by the sea.