This is a very broad question that depends on what you are looking for here are a few highlights relating to places in London which I have recently visited that were much better than expected:
Although a little more expensive than standards cinemas (tickets around £13) the IMAX on London’s Southbank is simply breathtaking with a screen over 20 metres high! (nearly the height of five double-decker buses)
Shunt is a great nightclub hidden away under/inside London Bridge Station. This is a perfect example of the kind of place you wouldn’t know was there unless you got invited or heard about it from a friend. The club is situated in the old storage silo of London Bridge Station and is massive once inside, well worth a visit for a strange random night out.
Columbia Road Flower Market
Is in East London and runs on Sunday morning. It takes place on (surprisingly) Columbia Road and consists of lots of locals selling flowers. The market is pretty cheap and has lots of nice little shops open to there are lots of photos of the market on flickr which give you an idea of what’s its like. This is a nice place to go on lazy Sunday afternoons before heading to a local East End pub for some grub.
Another East London classic Brick Lane is walking distance from Liverpool Street Station and features some of the best and cheapest curry houses in London. The area is full of trendy bars, restaurants and nightclubs. Check out Brick Lane on a Sunday to see the arts and craft markets and loads of great food stalls.
Billed as the biggest shopping centre in Europe, Westfield London’s size is astonishing. Personally I am still not quite sure why London needs a mammoth shopping centre but it’s still good fun none the less. Probably best to go when sales are on or during off-peak shopping hours to avoid the shopping masses.