Perhaps your time is limited and you need to keep an eye on the checkbook, but you're looking for a family vacation with a hint of the elegant - not a scrimping and saving, camping-out, doing-it-in-the-rough sort of venture. For our family, the occasion was the conjunction of a silver anniversary with a teen-ager going away to college. Somehow a trip abroad or to a seaside resort just didn't seem to be what was called for.

How about a cruise, a one-week luxury ocean-liner spin into the Caribbean? we said. For two teen-age daughters, a working wife yearning for relief from a particularly chilling New England winter, and good ol' Dad who believes there must be something redemptive about a family who sails together, this was just the ticket.

And the SS Norway - the reconditioned and repolished SS France - looked especially appealing. The Norway, the star of Norwegian Caribbean Lines five-ship cruise convoy, is awesome - a gigantic floating hotel-entertainment complex: 70,000 tons, 12 decks high, the length of three football fields. And it berths 1,850 passengers. Our late-February sailing was almost fully booked.

Too big? Perhaps for some. But we found there was something for everybody - families with young children, young mod marrieds, singles, teen-agers, even babies. And there is plenty of room for everyone.

Activities escalate from swimming, lazing, dozing, and reading to more active sports - among them volleyball, golf-ball driving, and offship snorkling in the all-ages ''dive in'' program.

While many cruise ships offer lounge and home-grown musical attractions, the Norway sports the likes of ''name'' stars, such as Jack Jones, Dihann Carroll, Jack Carter, Robert Goulet, and Phyllis Diller in Las Vegas-type revues (a bit more ''PG'' than ''R''), along with first-run movies (we viewed ''On Golden Pond'' between sunnings) and nightly disco for the with-it set.

But there is also the traditional table tennis and shuffleboard, bridge and cribbage, and an assortment of lectures ranging from speed reading and beauty tips to sports lore.

Expectedly, food abounds. But here again, variety is the fare. Formal (tux and long gowns if you like, but not necessary) nine-course dinners in the two nicely decorated dining rooms to on-deck hot dog, hamburger, salad buffet lunches.

The food is at least semigourmet: Cornish hen, capon, choice steak, and prime rib; succulent fish dishes; vegetables with tasty sauces. And of course, rich, rich desserts. As former Californians who have endured five produce-scarce Massachusetts winters, we particularly opted for the melon, fresh berries, and daily assortment of peaches, pears, plums, grapes, and apples.

We were a little snobbish about the Florida warm-weather lobster (once you have been weaned on a Maine lobster, you get that way). The food, well-served by immaculate Jamaican waiters with good humor but proper reserve, came in steaming; beverages were piping hot.

The Norway has 18 cabin categories - and so a size and price for all. Veteran cruisers advise outside cabins (for light), preferably located midship (for less motion during rocky seas). We booked late and had to take what was available. We ended up with two bunk-bed inside cabins forward in the ship. They were small but sufficient, nicely decorated, and kept spotlessly clean by stewards who attended to them twice a day. We liked the separate closets and closed-circuit television that kept us up on world news, ship activities, and even offered current movies. A nice extra: heated towel racks in the bathroom. But, alas, there always seemed to be a dearth of large beach towels.

It might be advisable to book early and pay a little more for an outside cabin.

The price of the cabin, of course, determines the major part of the cost of the cruise. The Norway's scale is perhaps less than what one might expect for this type of luxury cruise. Our table mate, a real estate consultant in southern California, made an analytical study of costs, accommodations, itinerary, comparative benefits with other cruises before he and his new bride signed up for the trip. By his estimates, Norwegian-Caribbean got considerably higher grades than comparable lines for one-week journeys.

Through 1982, the Norway offers accommodations for as little as $870 a person. Families with children under 16 get a discount. And, of course, group and charter rates are also available. On the other hand, suites start at $1,700 and run to $2,280. Air fare is extra. But sharp shoppers can usually find cut rates to Florida year-round. And combination air-sea packages are offered also.

In budgeting, it is well to plan for $5 a day per person for tips to room stewards and dining room personnel. Tips can be a problem. Taxi drivers and dock hands often have their hands out. Reasonable tipping is expected. But don't be pressured into overdoing gratuities.

Travelers to the Caribbean are allowed generous duty-free allotments - about along the Norway's International deck ''Fifth Avenue'' and ''Champs-Elysees'' before searching for in-port bargains in St. Thomas and Nassau. During the seven-day cruise, the ship docks for a day at St. Thomas, overnight in Nassau, and (weather permitting) at a secluded Bahamian outisland for sun and surf.

My wife, Mary Lou, found good perfume and summer sportswear buys on ship - 20 percent off on many items. We combed St. Thomas for linens, specialty jewelry, and knickknacks. We found a beautiful large linen tablecloth with 12 napkins for comparable one in Boston for over $60). And our younger daughter, Laura, is very pleased with some gold earrings she found for under $20. I purchased a pair of Bahamian shirts for $12. We shied away from the watches and glassware, which seemed overpriced. But some of our fellow travelers insisted otherwise.

In Nassau, the word is ''straw'' - hats, bags, trinkets, suitcases, you name it. I bought a fedora for $4 by standing mum while the vendor lowered the price from $8. Mary Lou cornered a large zippered straw bag for $6 - by any standards a bargain.

Ship stores will usually take personal along with traveler's checks. But cash is usually needed on the islands. It is well to store monies in the pursers' safe-deposit boxes and exchange checks for cash just before heading for port.

One of our nicest days ashore was on Great Stirrup Key, an outisland leased by the cruise line for a beach day. The youngsters joined the ''dive in'' program, leased snorkling equipment and cameras, and spent hours searching the wonders of the ocean bottom. Along the palm-lined sandy beach, picnic lunches were served. We swam, splashed, and sunned amid native calypso sounds. The authenticity is just a little spoiled by native vendors who have set up impromptu stands with brightly colored cloth and trinkets. The commercial aspect seems a bit offensive in this atmosphere. But while buyers abound, it will remain.

Of course, there are no tours on Great Stirrup Key as there were on St. Thomas and Nassau. This is a good way to get an overview of St. Thomas and a glimpse of historic Bluebeard's Castle, Charlotte Amalie Harbor, and the fascinating Coral World. Depending on the package you choose, prices run from $8 to $26 a person. We opted for on-our-own shopping. Some who joined the tour were satisfied. Others felt unfulfilled.

The Nassau tours (from $16.50 to $27 a person) are nightclublike in atmosphere. Many passengers felt the ship's entertainment surpassed the island calypso show. Drinks and gambling are also highlighted in this particular outing.

The law allows the Norway to maintain a gambling casino when the ship is at sea. But it is off the beaten track, and nongamblers need not feel uncomfortable about it.

Liquor is available at dinner and on deck. But fortunately, it is not pushed on those who don't imbibe. In fact, fruit juices are always available, even in the lounges. Soft drinks are served at meals for a nominal 50-cent charge, in the disco and on deck for 75 cents. Both dining rooms have ample nonsmokers sections.

Also of importance: The Norway has more than enough party facilities. But it is not considered (by veteran cruise takers) a ''party ship.'' Others have a different reputation.

All in all, the Norway is an elegant ship with a broad variety of accommodations and activities to fit different tastes. And for a cruise of this type, the price is right. Practical information:

Prices for this Caribbean cruise on the SS Norway range from $870 to $2280, for the fall and winter months, with an average of $1200. From Jan. 22 through March 26, 1983 prices will range from $975 to $2650 with an average of $1350, and after April 1, 1983, prices will range from $955 through $2575, with an average cost of $1300.

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