AT FIRST report it sounded too good to be true. For about $20 more apiece, our routine vacation trip to the islands could be turned into a kind of jet-powered travel grab bag: three weeks of virtually unlimited travel everywhere from Boston to Barbados, from Seattle to San Juan.

The instrument was Eastern Air Line's new Unlimited Mileage Fare, inaugurated Sept. 10, which allows two persons traveling together to fly anywhere Eastern flies in the United States, Mexico and the Caribbean for three weeks for a maximum of $323 each.

And that's a lot of places: 101 cities and 11 countries, including Jamaica, Bermuda, the Bahamas, Santo Domingo, St. Thomas, Acapulco and Trinidad.

The basic restrictions seemed eminently sensible: At least three stopovers are required, the traveler can't return to a visited city except to change planes, and final reservations must be paid for and set in concrete two weeks before departure. The basic fare varies roughly from $302 to $323 per person, depending on such minutiae as departure taxes, fuel surcharges, etc.

Certain peak holiday travel periods are blacked out. And that's about it.

The first impulse, of course, was to drool over that map and decide to eat the whole thing. We'll crash for a few days in Acapulco, I decided, then up to Seattle and over to Boston, down to New Orleans, across to San Juan and wind up with a whirlwind Caribbean extravaganza - Montego Bay, St. Thomas, Antigua, St. Lucia, Barbados and Trinidad.

Eastern's actually had some people try to do that, including a disc jockey from Tampa attempting to jet his way into the Guinness Book of Records (he made it: 22 stops in 21 days, 121 hours in the air) and a couple of medical students from Dallas who shopped for hospital residencies throughout the East during the weeks and spent their weekends in the islands. (It's possible to rack up a few thousand dollars in comparable air fares.)

But unless your idea of relaxation is running through airports every day like O.J. Simpson, you may prefer a less ambitious travel schedule.

Since we had only 14 days, we reluctantly pared our itinerary to three stops - Jamaica, St. Thomas (continuing on by non-Eastern means to Tortola in the British Virgin Islands) and Puerto Rico. But even at that we discovered one of the major nettles in the Unlimited Mileage Plan: fewer stops don't necessarily mean less travel.

Even when it serves the points to which you want to travel, a single airline rarely follows the exact route or timetable you want. Thus, in order to fly from Jamaica, our first stop, to St. Thomas, we found we had to fly BACK to Miami from Montego Bay, spend the night in Miami, fly to San Juan, spend the night there, and then get a plane out the next day.

It would have been far smarter, in retrospect, to let the Eastern timetable dictate not only the routing, but the sequence of the stops and, possibly, the destinations as well, so as to minimize airport hassles.

Because every stop means more standing in line and more opportunities for lost baggage, incompetent service, plastic meals, crowded planes and opportunities to explain to the security guard that the diving knife in your carry-on luggage won't be used to hijack the plane.

With the exception of that first free-at-last liftoff that starts your vacation, getting from one place to another is rarely and fun, if only because it so duplicates the rat race you probably left home to escape.

But with those cautions in mind, the traveler hungry for new places can find the Unlimited Mileage Plan an invaluable passport to discovery.

Had it not been for the freebies of the plan, for example, we wouldn't have taken a chance on Jamaica, which we had been warned against because of the highly publicized political and - allegedly - racial problems of the island.

(According to Richard P. Ramaglia, executive vice president of the American Society of Travel Agents, Jamaican authorities have made "substantial improvements" following some reports of harrassment of tourists. Jamaican officials met recently with ASTA in New York following receipt of a letter from the travel agents requesting information. Ramaglia described ASTA's inquiry as a "routine action" that has been taken in a number of cases in other areas where tourists experienced difficulties.

(Jamaica has created the post of "assitant police commissioner solely to review the circumstances in the event of an arrest or detainment of any foreign visitor," Ramaglia said, and to deal with any possible problems that might involve tourists. "On-going communication" has been established between Jamaican authorities and ASTA's office of consumer affairs, Ramaglia added.)

Drunk with the power of unlimited travel, we impulsively flew to Montego Bay, rented a car, and drove along the brilliant, sun-washed north coast to Ocho Rios, past the shuttered, once-splendid hideaways of a former, colonial day.

That Jamaica - the land of transplanted British culture, carefree natives and tropical posh - no longer exists, if indeed it ever did. In its place is a society no less fascinating or comfortable, requiring only a traveler's willingness to meet it halfway.

Armed with a Jamaican friend's list of local dishes to try, for example, we found that Jamaican cuisine is not only the cheapest on the island, it is usually the best. And while a meal of curried goat and Red Stripe beer in Ocho Rios Parkway Restaurant ($6 for two) may not suit everyone, the locals we met appeared astonished and delighted at the prospect of tourists appreciating something so thoroughly their own.

Everywhere we went iN Montego Bay and Ocho Rios we found Jamaicans - while not servile - both courteous and helpful, and extraordinarily aware of the importance of tourism to the future of the island.

The discovery of the Jamaican people - even more than the beaches, orchids and waterfalls of the island - would have been enough to justify the Unlimited Mileage Plan.

But the plan also proved a way to eliminate places we only thought we wanted to go. We found, for example, that Tortola, where we had gone to SCUBA dive, had virtually useless facilities, both expensive and undependable, while St. Thomas - just a few miles away - had multitudes of diving opportunities and cheaper programs. As beautiful and peaceful as the British Virgins are, next time we'll make plans to dive from St. Thomas.

And in the end, even the extra stops proved fruitful: serendipity, after all, is the name of the travel game. Our brief overnight stay in Miami led us to a new high-rise Sheraton near the airport which proved, with its bright prints, wicker furniture and good food, a surprisingly soothing place.

Likewise, our San Juan stopover led us to Hotel El Convento, a beautifully restored 18th-century convent in old San Juan, where $45 a night bought access to a fountain-filled courtyard bright with awnings, and a high-ceilinged room whose antique charm glowed through occasionally spotty housekeeping. We were so taken with the place, we returned on the Puerto Rican leg of the journey to while away our days among the asapaos and pina coladas of Old San Juan.

Eastern says more than 33,000 people have taken advantage of the Unlimited Mileage Plan since the airline inaugurated it Sept. 11. The plan is due to expire next September, but Eastern has asked the Civil Aeronatics Board for an extension.

An Eastern spokesman says candidly that Eastern's plan was patterned after one started by Allegheny Airlines to cushion that carrier against recession-born cutbacks in business travel.

"The name of the game," the spokesman said, "is to get the non-business person traveling - people who wouldn't be flying if it weren't for a plan like this."

So far, the airlines say, it's working for them. It certainly worked for us.