You Londonians

..maybe any of you can recommend any nice places to visit for a first time visitor in London ? if i manage to earn enough cash before the summer i'm planning on flying to the big city and spend about a week or so there to try to experience some of it. I'm also wondering what a good relatively cheap place to live would be in the city or nearby, any suggestions tips or ideas would be very welcome.
Btw, i'm not trying to hijack the thread. Just asking because there's no one better to ask than you people who live and work there.
/ Max