Jamaica; WHITE SAND BEACHES FRINGED WITH PALMS

Dinner was under way on the candlelit terrace at Jamaica's Round Hill. Under palm and almond trees, waiters, some of whom have worked there 20 years or more, deftly served the delicacies for which the Round Hill cuisine is justly noted. In the shadows a guitarist and a pianist softly picked their way through a medley of Jamaica tunes.

A lovely setting, peopled by the well-bred, the well-spoken, and the well-heeled. Then, into the subdued light stepped a young couple, hand in hand. Matching T-shirts proclaimed their fealty to New York.

Across the terrace, Michael Kemp, Round Hill's manager, making his usual evening rounds, stood chatting at a table occupied by one of Britain's parliamentarians who, with his white-haired wife, was enjoying his annual Round Hill holiday.

With the radar sensitivity possessed by all expert hoteliers, Mr. Kemp excused himself and within seconds, menus in hand, was graciously escorting the newcomers to a table. Drawing out their chairs, he seated them, shorts, T-shirts , flip-flop sandals, and all.

Only a few years ago dinner at Round Hill was strictly coat and tie, even black tie. But times change and, as Kemp points out, times in Jamaica, at least in some aspects, have changed a lot.

''We still work hard at making Round Hill the most deluxe resort in Jamaica. But we've had some slim years, so today we're receptive to business that in the past we might have turned away.''

Kemp's attitude is amply reflected all through Jamaica, from Negril in the west to Port Antonio in the east. For the past two or three years the outlook of people whose livelihoods depend on tourism (next to bauxite, Jamaica's No. 1 revenue source) has been, to use a Jamaican expression, rather ''bleaky.'' Under Michael Manley's two successive administrations, tourism, for a host of complex reasons, fell to a record low. In 1980, however, Edward Seaga succeeded Mr. Manley as prime minister and these days the ''bleaky'' outlook of restaurateurs, merchants, and hoteliers is gradually giving way to cautious optimism. It's a situation which, in 1982, holds plenty of benefits for a Jamaica-bound tourist.

Long known as a playground for the wealthy and the superwealthy, Jamaica also abounds in attractive, modestly priced accommodations. Today a vacationer returning after an absence of several years, or a first-time visitor to the island, can look forward to a warm welcome by Jamaicans who are clearly delighted by the resurgence in tourism.

Jamaica, from the Arawak ''xaymaca,'' meaning land of wood and water, lies 700 miles south of Miami, one of the Caribbean islands nearest to US shores. The greatest concentrations of tourist facilities are strung out along its north coast, where the best beaches are to be found. The capital city, Kingston, a splendid deepwater port, is on the south coast with the Blue Mountains running in a ridge, down the full length of the island.

Most visitors fly into Montego Bay on the north coast. Nicknamed Mobay, it was more poetically dubbed El Golfo de Buen Tiempo (Fair Weather Bay) by that master name-giver, Christopher Columbus. It takes about an hour and a half to drive west from Montego Bay to the village of Negril, along a road that is one-half good, one-quarter not good, and one-quarter terrible.

In the 1960s and early '70s Negril underwent its first building boom. Fortunately, in a burst of ecological foresight, it was decreed that no hotel could rise higher than the tallest palm. Accordingly, Negril's beach, seven miles long, fringed the full length with coconut palms, remains unspoiled.

At the Coconut Cove, two couples can take a two-bedroom housekeeping apartment for $300 a night, breakfast and dinner included. It's a rate that covers airy, well-appointed accommodations, only a coconut's toss from the water's edge. Its cheerfully casual ambiance and friendly staff make it particularly appealing to families with children.

Just west of Montego Bay the 31-room Tryall Golf and Beach Club has just undergone a half-million-dollar spruce-up. All of its exceptionally spacious rooms overlook the 18-hole Tryall golf course, conceded to be the most beautiful in Jamaica. Tryall is built around one of the fabled Great Houses, one that dates back to 1835. Rates begin at $160 per person per day, breakfast and dinner included. In addition to its par-71 course, there are six tennis courts and a fine beach. The Tryall property covers 3,000 acres of lush Jamaica countryside. Discreetly tucked away behind hedges of hibiscus and stands of lime trees are 40 handsome villas of varying sizes. These too are available for leasing, one week minimum, fully staffed, starting at $1,500 a week.

Round Hill is just down the road from Tryall, a couple of miles closer to Montego Bay. Round Hill is unabashed luxury, tasteful, comfortable, and proud of its high percentage of repeaters. Only a few years ago it was essential to reserve space as much as six months in advance. But the political unrest of 1980 affected Round Hill no less than other hotels. Reservations fell off and are only now picking up again. Round Hill, like Tryall, also offers villas for leasing, when the villa owner is not in residence. Unsurprisingly, Round Hill rates are expensive. Surprisingly, a good bargain is available this year between March 15 and April 15: Children under 21, accompanying their parents and occupying a separate room, will be charged half price.

The Montego Bay Crafts Market on the edge of town, vastly improved in recent years, is now tidily housed in individual booths and stocked to the gunwales with straw baskets, purses, hats, rugs, and some interesting carvings.

In Montego Bay proper on Sam Sharpe Square, not to be missed is The Cage. It's a tiny building, once a slave prison, open now to the public. Inside can be seen a poignant collection of artifacts, salvaged from the days of slavery, as well as an excellent collection of old prints depicting plantation life, each of them well mounted and framed for easy viewing.

Good restaurants are plentiful. The twin distinctions of best food and best location must probably be shared by Marguerite's-by-the-Sea, newly opened in December, and The Diplomat, high on the hills overlooking the lights of the harbor. Denise Brahan, a young American, is chef at the former. She has managed a neat and quite unique blend of Jamaican herbs and spices with French dishes, and the results are often gastronomic masterpieces. Like all of the diners, Ms. Brahan is charmed with the restaurant's location in what was once a private home , literally lapped by the sea. The Diplomat, on Queen's Drive, like Marguerite's , is also in a converted private home. There manager George Kahl plays to the hilt his role of gracious host, overseeing the service of food that is not only excellent but provided in a style that largely vanished with the 19th century. Both restaurants are open only for dinner, and reservations, given their growing popularity, are certainly advisable.

It's a 67-mile drive from Montego east to Ocho Rios, along a lovely shoreline with plenty of places to swim, picnic, or explore. One exceptionally interesting stopover is the restored Greenwood Great House, once the home of Elizabeth Barrett Browning's family. Robert Betton and his wife, its present owners, have lovingly brought back to life its clocks, music boxes, harp, organ, and piano. The half-hour tour they provide personally is nothing short of fascinating.

The well-known Half Moon Hotel and Golf Club is east of Montego along this same stretch of road. For more than 30 years it has attracted golfing enthusiasts with its 18-hole Robert Trent Jones golf course. Its complex of 13 tennis courts and its edge-of-the-sea location appeal to Canadians and Europeans quite as much as to Americans.

Ocho Rios, forever in hot competition with Montego Bay for the tourist's dollar, offers good shopping and good hotels and guesthouses in every price range and, of course, fine beaches. It also takes great regional pride in what it calls its ''natural attractions,'' by which is meant rafting on the Martha Brae and Rio Grande Rivers, the spectacular, cascading Dunn's River and Fern Gully, once a riverbed and now a dramatic canyon of tropical splendor.

Continuing on east of Ocho Rios, the route runs out to the sleepy town of Port Antonio where there are fewer inns and hotels but plenty of spectacular villas and private homes. Many of them here, and indeed along the whole length of the coast, are available for leasing through the owners' cooperative, JAVA (Jamaica Association of Villas and Apartments), with offices in Ocho Rios (974- 2508) as well as in New York ((212) 986-4317).

Along the entire coast there's also plenty of choice for the truly penny prudent. In Negril at Rock House, the tab for a cottage with kitchenette for two persons is $60 per night, with a weekly rate negotiable. Come nightfall, there's no electricity, but rather the pleasant buttery light of kerosene lanterns.

The Upper Deck on the hill overlooking Montego Bay offers scrupulously clean housekeeping apartments, at modest rates based on size. The Toby Inn, in Montego Bay proper, like the Upper Deck, welcomes back year after year vacationers who appreciate its $50 per room, per night price tag as well as the eagle-eyed maintenance provided by the Chins who own and run it.

Naturally hospitable, the islanders have emerged from the economic hardships of the past few years more eager than ever to welcome Americans to their homeland. Almost every tourist facility operates right through the summer, and the sharp drop in rates after April 15 heightens the attraction of Jamaica as a vacation choice.

In the leafy churchyard of St. James parish church in Montego Bay a headstone describes members of a family as ''lovely and pleasant in their lives. . . .'' The words seem as well matched today with the people of Jamaica as when they were inscribed there 150 years ago.