When I was there a couple years ago, we stayed at the
Radisson Edwardian Kenilworth hotel. (link goes to the Radisson Edwardian general site, there are several in London) I liked it. The room wasn't gigantic but three of us fit in it, it was in a great location next to the British Museum and a block away from the Tottenham Court Road tube station.
I would advise that if you can, take the tube from the airport into the city rather than a taxi. It's very convenient and you'll save a bunch of money.
I love London.
