As far as sightseeing goes, if you're a first-timer, see Buckingham Palace, Westminster Abbey, Tower Bridge, Big Ben, St. Paul's Cathedral, Trafalgar Square, and kiss your mate in Piccadilly Circus just to say you did it (the little statue of Eros represents the god of love). Dozens of tour companies offer "discover London" packages aboard open-top, double-decker buses that make dozens of stops and depart every 15 minutes.
Evan Evans (+44-20-7950-1777) is the largest and most popular of these, and now offers lunch and dinner cruises on the Thames as well as packages throughout the British Isles to fit just about any schedule. Pick up their brochure at nearly any hotel or travel agency. Better yet, contact the British Tourist Authority (+44-20-8846-9000) before leaving the states so you have a better idea just what you want that itinerary to include, or try "gay friendly" City & Village Tours (+44-20-8858-5858) for a list of their services.
Just below the touristy, sightseeing surface of governmental and royal landmarks, London is a city rich in galleries and theaters. Tate Britain (Millbank, Pimlico Tube, SW1; +44-20-7887-8888), for example, houses an outstanding permanent collection of British masters from the sixteenth century to the present, an overwhelming Turner collection, and a selection of 20th-century painting and sculpture heavy on cubism and surrealism. The Victoria and Albert Museum (Cromwell Rd., SW7; +44-20-7942-2000) has a changing display of the some of the world's most outstanding achievements in applied and decorative arts and architecture.
Beyond these, there is of course the British Museum, the National Gallery, the National Portrait Gallery, and the (not to be missed) Shakespearean replica Globe Theater. Kensington Palace houses the royal dress collection, including coronation gowns and wedding dresses. Guided tours are given every hour -- they are very informative and camp.