Take a walk on Hampstead Heath and enjoy the view over London from the hill. Camden market at the weekend.

Piccadilly Backpackers gets generally bad reviews here - most people seem to prefer The Generator if it's a young, partyish hostel you're looking for. The Generator isn't quite so central (but it is close to a Tube station and, as it happens, close also to the British Museum).
For one-day visitors, people often recommend the hop-on hop-off tourist buses to get a good overview of the city.

Just back from London and I would thoroughly recommend Tate Modern. Free to get into and its huge inside and so interesting. Would also recommend the restaurant on the top floor as well, slightly pricey but good food and amazing views. Borough Market is nearby which is worth a look too.
Also recommend Camden Market. Lots of cool things to buy.

I stayed at the Piccadilly Backpackers Hostel a few years back. The service was pretty poor, with them not giving us the room we paid for initially and then the cleaning staff bursting in on us. Otherwise the price was right and the location was great. I do remember the hostel being hard to find from the tube station initially do to the lay out of the area.
