I personally wouldnt bother with the V&A museum, i found it boring as f**k... But then I'm uncultured. The Science museum and the Natural History museum are both pretty damn good, as is the Tate Modern. As for shows/theatre trips, they tend to be well-f**king-expensive (£40 a ticket to some of the ones i've been to) so its worth booking ahead/getting last minute deals/going to a slightly less well known show. If you get bored for a place to wander round, get the Jubilee line from London Bridge to Canary Wharf (3 stops) as thats a generally nice area with a big shopping centre, nice bars/resturants and is a great place to go exotic car/rich people spotting. The London Eye is another thing you could think about, thats on the Southbank and is pretty easy to eyeball. Have fun!