If you're going Central London, then most places are pretty damn famous lol... however... If you feel like a trip on the Docklands Light Railway (DLR) there are no drivers (except in bad weather) and get yourself to Greenwich. It's a suburb of London and quite a posh area. Go to the Old Royal Naval College for a start, because it's one of the most beautiful sites in London, and look in the Painted Hall and Chapel. There's signs everywhere pointing towards them. Also (being biased) Trinity College of Music is right opposite and on a Saturday the Junior college is on (that's why I'm biased) and there's main college in the week. Don't forget the Royal Observatory or Museum.
HAVE FUN!!!!!
