London is an absolutely incredible, and large city, so you won't have any trouble finding things to do. Obviously you have to hit the main places: Big Ben, Westminster Abbey, Tower of London, Buckingham Palace, and Parliment.
Some things that are also worth your while would be Abbey Road, Camden Market, Winston Churchill muesuem, etc. You will be able to find so much to do!
I also highly, highly recommend going to see a show in London! I saw Les Miserables and it was one of the best things that I did.
I would highly recommend trying to get to know the Tube if you go. That will be your best friend when trying to navigate the city.
Also, London is on the British Pound, so make sure you know the conversion rate, and how much monye you think that you will be spending. Recently, the pound has been incredibly expensive. That's definitely something to keep in mind!
London has some of the best food ever. They are known for their Indian, so definitely try that! If you go to Camden Market, you will be able to browse through a lot of different genres of food, and they are all absolutely delicious!