What dates are you in London for??
If you want to see all the tourist things and see lots of London the best thing to do is one of the Tourist buses, they take you to all the main tourist attractions and you can get on/off when you want.
If you're in Camden there is the Market but it's not the best market -I'd go to Spitalfieds or Portobello Markets over Camden Market. The Lock Tavern in Camden is a really good pub - does fab roasts on Sundays and good food the other days and they have DJs who play really eclectic stuff.
Go for a wander around Brick Lane/Hoxton/Shoreditch (East London) - lots of nice little bars/restaurants and one-off vintage shops, also Spitalfields Market is there. The Big Chill bar on Brick Lane is a nice way to spend an afternoon - does good food and various DJs.
Similarly Notting Hill is nice to wander around and if you go at a weekend you can combine it with Portobello Market.
More centrally, Soho has a good mix of one-off shops, record shops, bars and restaurants.
Avoid places like Leicester Square and most of Oxford Street cos they are full of tat.
Re clubbing what kind of music are you into cos that will help in club suggestions??
Check out some traditional English restaurants, a visit to London isn't complete without fish, chips and mushies - my fave are either Geales in Notting Hill or Randall & Aubin in Soho.
The National History Museum and the Tate Modern are 2 of the most popular museums/galleries.
One thing to remember is that London is HUGE, rather than knacker yourself out trying to do everything it's probably best to plan each day so eg one day spend doing the traditional touristy stuff, one day in East London, one day in West London etc.
You're staying really central in Hyde Park (you're close to Knightsbridge, Park Lane and Oxford St) but you'll need to use public transport and public transport for tourists is a rip-off in London. The best thing to do is get an Oyster card when you arrive (you pay a depost to get one, I think it's £2) and then put say £20 on there when you arrive and then use that for tubes and buses. It works out MUCH cheaper than buying single tube fares every time you want to hop on a tube.
If you let us know more what you're into then we give some more specific suggestions.
Hope that helps