Here are some of my favorites:

Greenwich (take a Thames boat there and the Docklands Light Rail/tube back for an extra treat). All kinds of great stuff in a very small area. Go up to the observatory for sure - nice view of all of London, outdoor market, etc.

British Library - where else are you going to see the original Magna Carta, Gutenberg Bible, and a number of the Beatles original scores?

British Museum - must do at least once.

London Eye - worth the wait on a nice day.

Recent terrific restaurant - Red Fort in Soho. Soho is great to walk around in day or night.

Other great neighborhoods - Chelsea (check out Sloane St. for amazing windowshopping), Marylebone and others