Thank for taking the time to reply, Sophie.
I note that you've mentioned the Tower Bridge exhibition. I've not been since just after it first opened but my impression then was it was over-priced and not really worth the visit.
One of the best ways to see the sights is to take a short river trip. I'm not suggesting one of the big tourist boats, which cruise for a few hours and cost mega-bucks; instead I suggest just using the smaller river buses. See here:
http://www.tfl.gov.uk...bankment-woolwich.pdf
The fares are reasonable, with any single trip costing £5.30 at regular prices, £4.90 if you've got an Oyster Card or just £3.55 with a Travelcard. It takes about half an hour to go from the Tower of London to the London Eye (which enables you to see a lot of the main sights on the way).
If you're in Trafalgar Square and think that the National Gallery might take up a bit too much time, pop down the (right hand) side to the entrance to the National Portrait Gallery; it gets far less crowded than the National Gallery. Don't be put off by the idea of 'portraits'. It's not just full of stuffy old oil paintings of people you've never heard of. Instead, if you head to the right galleries, you'll also find some stunning photography. Admission to the NPG is free.
If you'll be seeking good food at cheap prices, take a look at this menu from Bistro 1 (which I love):
http://www.bistro1.co.uk/bistro1/Menu.html
(Click 'Branches' to see where they are. I always use the one in Southampton Street, Covent Garden).
Chris