Madame Tussauds - the ultimate tourist attraction. I wish they had more of the behind-the-scenes stuff. That was more interesting to me than just looking at figures.
Kensington Gardens - I sat near an old guy who was feeding birds. He was wearing a hat and they kept jumping out of the hedge behind him to sit on his head and that hat never moved an inch LOL
I waited to the side while a friend took pictures including several where he laid on the ground right up next to the clock tower so he could get a unique perspective :)
Instead of going as a tourist, go when they're having mass or evensong or any other event. The singing there is magical, and you feel part of the place, the history.