If you haven't booked a place to stay, I highly recommend the Marriott County Hall. Sits at the southside base of Westminster Bridge in a building which has been the backdrop in many movies. Members of many foreign services stay there because it is just across the bridge from Parliment/Whitehall. Big Ben becomes your alarm clock. The Wheel is right next door, and a Tube station that looks like it came out of the movie
Brazil is just across the bridge. Waterloo Station is two blocks away, and the Theater district is a 10 minute walk across the Hungerford Bridge to the east on the bend of the Thames. There's a Dali exhibit along the waterfront. You will pay more...much more, but you will never find a better place to stay.
http://www.marriott.com/hotels/trave...l-county-hall/
Everything is right there...Westminster Abbey, Trafalger Square's a short walk with the Art Museum on it, and the British Museum (assolutely need to go there) a few steps beyond that.
One of the greatest indoor junkyards is at Vicky and Al's (Victoria and Albert Museum) a bit west of Harrod's (eat in the bottom floor "deli" or in one of the upstairs cafes) which is not far from Buckingham Palace. The Tower's a stop or three on the Tube, as is St. Paul's.
Take a big red double decker bus around on the first day...muy goodo. Take the Tube and the London cabs everywhere else.
The Marriott will get you a car for the day...the driving is not bad at all. Go out to Windsor Castle...neat little town below. West to Bath, and then south to them old stones and back again was a great one day trip.