National Gallery and the British Museum, they are musts. Also the Churchill War Rooms are very worthwhile. In my opinion, the British Museum is without equal.

To get the most out of the National Gallery and the British Museum, check into a guided tour--they're offered daily by both and are free. A guide can highlight the museum in a relatively short period and you can then return on your own for things you're interested in. Without a guide, you can wander the entire day and never see such treasures as the Rosetta Stone and the Elgin Friezes.

Also, London Walks, http://www.walks.com, does wonderful walks throughout London. They generally run about 1 1/2 hours in length and you will see things you would otherwise miss. The guides are excellent. Many have theatre experience and are members of the Royal Shakespeare Theatre.