Check out china town for an interesting experience - it helps if you like chinese food obviously but the service is generally good and the food is fantastic. There's also quite a lot of shops and such to look around, you could probably pass away a happy couple of hours there (at least, if its your scene).
Failing that theres the obvious sights... tower bridge, the London Eye / Dome (bah), Big Ben...Canary Wharf and St Pauls Cathedral. Not bad if buildings is what floats your boat.
Uh...there's also some good cinemas around but being central London you can expect to pay quite steep prices for them - again that should be an easy way to waste a few hours.
To be honest I'm not sure how late shops close in London (I rarely stay out late there unless I'm going to a gig or something) but the chances are that something will be open, Harrods and such are there of course and you can definitely waste some time in there - there's always something to look at.
Funny really.. I should know about the place, living close and all, but I really couldn't recommend anything better. Heh... good luck - if you've any questios feel free to ask
