There's many things.
Going on the London Eye, shopping at Oxford Street, St. Katherine Docks, Hyde Park, Camden Market, The o2, Canary Wharf
Tired of typing now
yeah i'm bored of london already - just feels like a really huge high street with lots and lots of bars after living here for a while.
The Science Museum is good.
If you haven't been there before, there is a wonderful Japanese restaurant called Zipangus not too far away from Leicester Square station.
The Japan Center isn't too far from the Troc, across the road and a bit further up the street. That has some nice stuff in... an another restaurant inside but I <3 Zipangus too much to even bother.
China Town is always a good place to walk through... even better when you stop off at the New Loon Moon supermarket to pick up some packs of delicious Pocky for like, 70p a box... which is about 3x less than what the shop down the road from it charges. :]