Go to
Soho, definitely, it's a fantastic place and the food is great.
Camden Market - speaks for itself really, go have a look around it has all the weird alternative stuff you'll ever need.
Huntarian Museum - A liiiitle tricky to find but it's definitely worth it. If you're into anatomy and babies in jars.
London Dungeon - creepy but oh so entertaining, if you're into spooky stuff you should deffinitely check it out.
Natural History Museum - Science. Presented in the coolest way possible. Like walking-inside-of-meteor-cool.
Madame Tussauds - They have some amazing waxwork but you have to pay and the queue is usually long so be prepared.
Tate Modern - if you're into modern art. Sometimes they have some awesome exhibitions around, it's worth checking out.
Embankment area - Just walking along the river is fun enough, you get loads of people performing weird things.
Covent Garden - close to Embankment, lots of shops and performers. Oh and a pub RYLers used to go to a lot :P
Hampstead Heath/Kenwood - Blatantly biased cos' I live near the area. Huge park with an amazing cafeteria where they sell like THE best cakes in the world.
Hyde Park - central London, easy to get to. Park. Nice Park, worth going to :]
West End - Our Very own Champs Ellysees, although not nearly as glamorous unless you venture deep into Regent's Street. THE place to get your shopping done
S'about all I can think about.
There's always the London Eye, The Portait Galleries, The Tower of London etc etc but the stuff I listed above is much more fun :]
Have fun!