Last time i went to london, I stopped at the Tate Modern Art Gallery, it didn't look like anyone else mentioned it so i thought i would, I'm not one for art gallerys that much, but this one was pretty nice, it had enough stuff to keep me busy looking for hours. Another gallery i went to was the dali museum, i think it might have only been there for a short time, but if not, it was right next to the eye, which is a must. That thing is huge, i think the tallest thing in london, you can see everything including the country outside of london. But plan on getting thier early, or have you family pick you up some tickets in advance. I think there is a few day que/wait for tickets. You also need to get there an hour or so before your time to ride. Its well worth the wait, you will have fun. Nothing like being trapped in a glass bubble with 15 or so strangers

EDIT: yes, the big red bus is the best bang for your buck. you can get to everything else for a very low fee.