For a treasure-trove of London culture, try the Barbican

OK, the dollar is strong, tourism is up, and you've decided to come to London - again. Or maybe, happily, for the first time. And all your well-meaning, and presumably well-traveled, friends and relatives have loaded you down with ''By all means don't miss Trafalgar Square and the National Gallery and the Tower of London and the crown jewels, and then there's the London Symphony and of course the theater and then right around the corner there is this darling little place . . . .''

And so it goes, until you have a list a mile long that even the most culturally attuned bon vivant may find daunting. Or possibly you have already encountered these not-to-be-missed watering holes and are just wondering what's new about London.

Happily there is a way around these traveler dilemmas - or at least an alternative to racing or retracing your way from one famous site to another. It's called the Barbican Centre, and quite possibly it is the best encapsulation of London culture you're likely to find.

Less than two years old and rising smack in the middle of the City, London's version of Wall Street, the controversial Barbican - 11 years in the making and (STR)100 million over budget - is now the permanent home of the Royal Shakespeare Company and the London Symphony Orchestra.

''One of the most argued decisions in the history of the British Council,'' according to Barbican administrator Henry Wrong, the center was intended to create a genuine neighborhood within the City by introducing an architecturally stimulating combination of arts complex, school, and conference center. Wrong likens the Barbican to such world class arts complexes as New York's Lincoln Center.

Included within the Barbican's vast confines are the Guildhall School of Music and Drama, an art gallery, a sculpture court, three cinemas, a public library, two restaurants, and 86,000 square feet of exhibition space - the largest such space in central London. If for no other reason than the center is new, large, air-conditioned, and open late at night, it should be more than a little palatable to visiting Americans.

Unfortunately, despite its having won the annual British Tourist Authority award and playing to near capacity audiences, the Barbican is being treated by many of the locals as some brash newcomer in a town that prides itself on centuries-old traditions. People here complain that is too big, too impersonal, too similar to the South Bank arts complex, too hard to find, and a veritable maze once you do find it.

True, the center is large - 10 stories of reinforced concrete - and it is in the middle of the financial district, which does get a tad deserted after 5 o'clock. But none of this truly detracts from the essence of the Barbican - that it is a treasure-trove of culture all under one roof.

It is virtually impossible to be bored here. During any given week there are noontime concerts or lectures, art exhibits, films, four or five Royal Shakespeare productions in repertory, and a concert schedule that changes daily.

If nothing else, there are plenty of clean lavatories and lots of big, inviting couches tucked around the foyers which are just perfect for plopping down on after a long morning of sightseeing.

For the visitor interested in one-stop culture or who wants to see a lot of the arts in a short amount of time and space, the Barbican Centre is ideal. It's not cute or quaint, but it's comfortable, modern, and offers some of the best cultural options in town.

On a recent blustery and chilly London day, this visitor found the ''concrete monolith'' a most hospitable retreat. Keep in mind that you, like the rest of London, will probably get lost, if not trying to get to the center, once you actually arrive. But this can be part of its charm.

Take the Tube to either the Barbican (simple so far) or Moorgate stops and then ask for directions. Try to follow the signs - there are several - but you will inevitably become disoriented the closer you get to the vast brick expanses that signal the approach of the center. (Remember that this a (STR)150 million ( several high-rise apartments.) Or give up and take a cab.

As it is difficult to locate the main entrance, simply enter from any angle. Immediately inside there will be more signs telling you where you are and where you want to be, such as the cinemas, main stage, or concert hall.

Although technically underground - only half the 10 stories are above ground - the two main auditoriums have been designed with spatial effects of height and breadth and decorated with warm, rich colors.

Both the 2,000-seat concert hall and the 1,100-seat theater use a raked tier seating arrangement to great effect. There are excellent sightlines in both, and in the theater - a revolutionary design - no seat is more than 65 feet from the stage. The concert hall is wood paneled and considered to have natural acoustics which have been improved in recent months. The theater is rarely ''dark,'' although a performance may be sold out. The Royal Shakespeare averages a 94 percent capacity, with ticket prices for the main stage ranging from (STR)2 to (STR)9.50 (about $3 to $14).

Over the year, the Barbican Hall hosts roughly 100 performances by the London Symphony under the musical direction of Claudio Abbado, and 200 more concerts by such visiting performers as the Vienna Philharmonic Orchestra, Kiri Te Kanawa, and Yehudi Menuhin. Other, more popular artists, such as Andy Williams and James Galway, have also performed here. And free noontime concerts are given frequently on the concourses.

Downstairs is the Royal Shakespeare's smaller, 200-seat theater, whose more experimental works, such as an anonymous 16th-century drama, ''Arden of Faversham,'' often get more enthusiastic reviews than those larger productions upstairs. All pit seats are (STR)4.50 and unreserved. In Cinema 1, such offbeat programs as a Francis Coppola retrospective or ''Roger Corman Day'' are featured , along with first-run films.

But there is more to the Barbican than seeing a performance, as many who live or work nearby are discovering. In fact much of the center's appeal lies in its architectural ability to lure you onward and inward - here a large glittery lobby reminiscent of a grand hotel, there a winding narrow stairway leading to the art gallery.

During my visit, three exhibits were running concurrently: a Matthew Smith retrospective, the Tolly Cobbold-Eastern Arts National Exhibition, and an open-air Giulio Ciniglia sculpture display. Beginning in February there will be a new exhibition of American folk art and next autumn a retrospective of James Tissot.

But possibly the most unusual part of the center is the public library. Spacious and multileveled, the library is a wonderfully imaginative facility that, not surprisingly, concentrates on the arts.

Within the separate music, film, and arts sections one can browse through play scripts, music scores, or art books. In the general section there are lots of useful materials like travel guides and maps of Britain. And in the children's library - the first of its kind in the City - the card catalogs are thoughtfully close to the ground. There are also low bins full of picture books and short carpeted steps just right for perching on. For a building that has been dubbed by some as ''Soviet in style,'' the interior of the Barbican is a remarkably cozy and inviting place.

As for the restaurants, there are two which, after rather dismal starts, have established relatively good reputations. The Waterside Cafe is just that - a buffet lunch or tearoom abutting the fountain-studded Lakeside Terrace. Outside, it is a bracing or balmy way to dine, depending on the capricious London weather. Inside it is less enchanting, with bright overhead lighting, lots of primary colors, and rather uncomfortable seats.

But upstairs, with a panoramic view of St. Paul's Cathedral and St. Giles, is The Cut Above. Billed as a carvery, this tonier of the two restaurants is awash in soft lights, pink tablecloths, and some lovely-looking slices of roast beef, turkey, and lamb. At a (STR)10 ($15) prix fixe, the three-course dinner proved to be some of the best traditional English cooking around. The restaurant also takes orders up to 30 minutes after the evening's last performance - something tourists will find very convenient and about as rare as the prime rib.

Other than that, concert- and theatergoers can subsist on ice creams during the intermission while they wander along the polished wood floors mingling with the other tourists, the British families dressed in somber wools, and the Bohemian-looking youth of London.

Only upon your departure - usually after 11 if you've been to the theater - will you feel the slightest bit desolate here in the City. That's when everyone slips through the electronic glass doors and makes a beeline for the car park or the tube stations. It's perfectly safe to walk, but infinitely more fun to jump into one of the black beetle cabs and dart away into the night.