If you're in the mood to for something really touristy, consider one of those hop-on-hop-off buses which stop at Paddington Station. Personally I would ride the Tube with a day pass. Don't forget changing of the guard at Buckingham Palace, 11:30 am every other day. You can visit the London Eye, Westminster, and Big Ben all one go (take the Circle line to Westminster station). I agree with previous recommendations for the British Museum, and admission is free.