For most visitors, a trip to London means a night or two at the theater. But increasingly, Americans are learning what the Brits have known for some time: Many of the best shows in town are not playing in the West End but at venues around town known collectively as Off-West End and the Fringe.

A little lesson in nomenclature. Off-West End includes North London's Almeida and Covent Garden's Donmar Warehouse, small theaters with worldwide reputations. Other Off-West End theaters of note are the Riverside Studios in Hammersmith, the Hampstead in Swiss Cottage, the Tricycle in Kilburn, and the Young Vic and Shakespeare's Globe, both on London's South Bank.

Then there are the Royal National Theatre, also on the South Bank, and the Royal Shakespeare Company (RSC), which has no permanent home in London at the moment. They are Britain's foremost theaters, and in a class by themselves.

Fringe theaters are often located in pubs or other spaces not built as theaters. The Bridewell, for instance, is in a red-brick Victorian building near St. Paul's Cathedral that once housed a swimming pool; the tiny, basement-level Jermyn Street Theatre is on a street off Picadilly better known for snooty shops selling custom-made men's clothing.

Fringe theater prices can be as low as $12 -- in contrast to the West End, where a ticket to a musical can cost $90, plus a booking fee. At the government-subsidized Royal National Theatre, for example, prices are $11 to $75. Real bargains are to be found at the National, where a special program, the Travelex Season, offers tickets to select shows for about $18.

There's still good theater to be seen in the West End, particularly "Anything Goes" at the Drury Lane and "Democracy" at Wyndham's, both transfers from the National, and Edward Albee's "The Goat, or Who Is Sylvia?" at the Apollo, a transfer from the Almeida. What a visitor needs to know, though, is where else to find interesting, well-done theater not far from the center of London. Here are some suggestions.

* Almeida Theatre. Almeida Street, Islington, 011-44-20-7359-4404, Tube: Highbury and Islington/Angel.

The recently renovated 321-seat North London theater has a well-deserved reputation for excellent productions starring big-name actors in edgy plays. "Whistling Psyche" by Sebastian Barry, a drama about Florence Nightingale starring Claire Bloom, runs through June 19. Tickets are about $10.75 to $49.25.

* Barbican Centre. Silk Street, 011-44-20-7638-8891, Tube: Barbican/Moorgate.

The Barbican hosts an eclectic selection of productions from overseas as well as plays by well-known London artists. Through June 19, Marianne Faithfull stars in "The Black Rider," theater artist Robert Wilson's take on Faust, with music by Tom Waits and words by Beat writer William Burroughs. "Jimmy," a solo piece about a hairdresser, runs June 23-July 3. "Gumboots," an extraordinary musical about South African miners who, because they were forbidden to speak under apartheid rules, developed a language by stomping with their boot-clad feet, runs July 6-10. "Amajuba," another South African musical, takes as its subject township life during apartheid and runs July 12-17. "Cirque Lili," a mime production, runs July 28-Aug. 15. "The Elephant Vanishes," adapted from stories by Japanese author Haruki Murakami, by the collaborative theater company Complicite, runs Sept. 2-25. Tickets are $15 to $60.

* Bridewell. Bride Lane, off Fleet Street, 011-44-20-7936-3456, Tube: Blackfriars, St. Paul's.

The far-from-posh auditorium looks conventional enough, but the stage covers what was in Victorian times a swimming pool and laundry. There's a remnant of that era in the bar: a large hand-powered mangle. Often an incubator for musicals, the Bridewell changes its tune this summer with "Burleigh Grimes," a drama about traders at a New York financial institution who live for sex, money and rock-and-roll (June 3-July 3). Tickets are $17 to $25.

* Donmar Warehouse. 41 Earlham St., 011-44-20-7369-1732, Tube: Covent Garden.

The 251-seat Covent Garden venue, along with the Royal National Theatre and the Almeida, tops most London theatergoers' lists. Like the Almeida, its productions are of the highest caliber and often include well-known actors. Through June 26, Francesca Annis and Ian McDiarmid star in a new version of Pirandello's "Henry IV" by Tom Stoppard. "Old Times" by Harold Pinter, starring Gina McKee and Jeremy Northam, runs July 6-Sept. 4, and the musical "Grand Hotel," with a cast to be announced, is slated for Nov. 29-Feb. 12, 2005. Tickets are $27 to $52.

* Globe. Bankside, 011-44-20-7401- 9919 or Ticketselect, 011-44-207- 850-8590, Tube: Blackfriars, Mansion House, Cannon Street and London Bridge, among others.

There is no theatrical experience like seeing one of Shakespeare's plays performed in this wooden replica of the 16th-century theater. Sit in the gallery, as the gentry did, if you like, but be sure to visit at some point during the performance the yard where "groundlings" stand. The theme of this season's plays, running through Sept. 26, is star-crossed lovers. "Romeo and Juliet" is currently running in repertory with "Much Ado About Nothing," and beginning June 18, "Measure for Measure." Tickets are $9 to $52.

* Hampstead Theatre. Eton Avenue, 011-44-20-7722-9301, Tube: Swiss Cottage.

Long an important part of the Fringe, the Hampstead only does new work. Authors who have premiered plays here include Michael Frayn, David Hare, Hanif Kureishi, Mike Leigh and Harold Pinter. Dael Orlandersmith's "Yellowman," about racism within the African American community, runs through June 19. Tickets are $23 to $38.

* Old Vic. Waterloo Road, 011-44-20-7369-1722, Tube: Waterloo.

Kevin Spacey, the latest in a long line of American actors to bring their talents to London, is the Old Vic's new artistic director. His first season begins with "Cloaca," Sept. 28-Dec. 11, a drama by Dutch playwright Maria Goos. The show many will want to see, though, is the Christmas pantomime "Aladdin," running Dec. 18-Jan. 22, 2005. Sean Mathias directs and -- this is going to be a hoot -- Ian McKellen camps it up as the Widow Twankey. Spacey will take to the stage in "National Anthems" (Feb. 8-April 23, 2005) and "The Philadelphia Story," in the Cary Grant role (May 3-July 23, 2005). Currently playing through July 31: Trevor Nunn's "Hamlet," with Ben Whishaw's performance in the title role causing much buzz. Tickets are $13 to $66.

* Regents Park Open Air Theatre, near Queen Mary's Garden. 011-44-8700- 601-811, Tube: Baker Street.

Running in repertory June 11-Sept. 8 are "A Midsummer Night's Dream," "Henry IV, Part I" (June 7-Sept. 11), "Camelot" (July 23-Sept. 4) and "The Wind in the Willows" (July 27-Aug. 21). Tickets are $16 to $40.

* Riverside Studios. Crisp Road, Hammersmith, 011-44-208-237-1111, Tube: Hammersmith.

Look for productions by two very fine companies who perform here: Shared Experience, which dramatizes 19th-century novels, and Complicite, a company known for its startling visual theater. "Roast Beef," June 8-27, transposes Greek mythic characters Clytemnestra, Iphegenia and Agamemnon into the 21st century. Tickets are $14.50 to $22. "The Wild Party," a musical set in Manhattan during the jazz age, runs July 27-Aug. 7. Tickets are $16 to $27.

* Royal Court. Sloane Square, 011-44-20-7565-5000, Tube: Sloane Square.

The Royal Court produces provocative new plays. "Shining City" by Conor McPherson (author of "The Weir") runs June 4-July 17; Simon Stephens's "Country Music," a crime story, runs June 28-July 17. Tickets are $13.50 to $50.

* Royal National Theatre. South Bank, 011-44-20-7452-3400 (information), 011-44-20-7452-3000 (box office), Tube: Waterloo.

The National should be at the top of any visitor's list: With three auditoriums, restaurants, bars, a bookstore and free pre-theater performances, the place hums day and night. Running in repertory this summer are "Cyrano de Bergerac," directed by Howard Davies and starring Stephen Rea, through June 24; "Measure for Measure," closes July 31; "The False Servant," a drama about sexual sparring during courtship, starring Charlotte Rampling, closes Sept. 15; "A Funny Thing Happened on the Way to the Forum," closes Nov. 2; and "The History Boys," a new play by Alan Bennett, closes Sept. 2. Tickets are $18 to $73. A special program, the Travelex Season, offers tickets for about $18 for some performances of "Forum," "Measure for Measure" and "Cyrano."

* Royal Shakespeare Company. 011-44-870-609-1110, Charing Cross or Embankment.

The RSC sends many of its productions from its home in Stratford-upon-Avon to London and, indeed, Washington. Until July 17, "Othello," with the incomparable Anthony Sher as Iago, is at Trafalgar Studios, at the former Whitehall Theatre (14 Whitehall, 011-44-207-369-1735 or 011-44-870-060-6632). Tickets are $36 to $65.

* Tricycle. 269 Kilburn High Rd., 011-44-207-328-1000. Tube: Kilburn.

Productions are diverse -- a South African musical played here successfully earlier this year. "Guantanamo: 'Honor Bound to Defend Freedom,' " taken from spoken evidence, runs through June 12. James Baldwin's "Blues for Mr. Charlie" follows, June 16-July 10. Tickets are $13.50 to $30.50.

* Young Vic 66, The Cut, 011-44-20-7928-6363, Tube: Waterloo or Southwark.

Because it is the artistic home of up-and-coming young actors and directors, the Young Vic is a favorite of some of London's most respected critics. Playing in repertory, Brecht's "The Exception to the Rule" and Ionesco's "The New Tenant," are part of Direct Action, a showcase for new directors, running through June 12. "Cruel and Tender," by Martin Crimp, after Sophocles's tragedy "Trachiniae," about terrorism in a city that has turned into rubble, runs June 17-July 10. Tickets are $36.

Susan Davidson is arts editor of Washingtonian magazine.

Who needs the West End when you can have Shakespeare's Globe Theatre?