Originally Posted by Mad About Drums
National Art Gallery (free)
St Paul's Cathedral
The Tower of London
The London Dungeon
Hyde Park (and Hyde Park Corner if you fancy doing some speech, lol)
Oxford Street (nice for shopping)
There's a big drum store called Professional Percussion in Kentish Town,
Agree with the above, although I think Pro Perc just closed. :(
Depends what else you like to do. There's also the Camden Markets, London Transport Museum/gift shop (at Covent Garden), music stores on Denmark St, shopping on Oxford St, Harrod's and Selfridge's depot stores are an experience, Beatles store on Baker St (I think right by Mme Tussaud's), and various (flea) markets throughout the week, incl Covent Garden daily.
And if you love Indian food, there are a million places to eat.
You'll find London is a very walkable city for the most part, but definitely a good idea to get a pass for the Underground.*
If you just want a feel for the city and some touristy stuff, a bus tour is also the way to go. My wife and I did that the first time we visited London, but have been on our own every trip since.
BTW, you will fall in love with London and the people. It's easily my favorite city of the 3 continents I've visited.
* I've got a list of my favorite stops, and the coresponding tube station... let me know. :)