Depends what kind of things you want to do or see, will you be staying in London?
There is so much to do to tourist wise in London, Buckingham Palace and changing of the guard, Tower of London, Westminster Abbey, St Paul's Cathedral, London Eye etc... You can get special bus tours which show you the sights and some give some discounts for entry but it can get quite expensive.
http://www.visitlondon.com/
http://www.theoriginaltour.com/
There are also some walking tours and nightime ones such as ghost tours.
http://www.london-ghost-walk.co.uk/
Seeing London at night is highly recommended, a walk by the river is free
Many museums are now free and I'd highly recommend the Science and History museum.
http://www.nhm.ac.uk/
http://www.sciencemuseum.org.uk/
There are also loads of galleries such as the Royal Academy and Tate.
http://www.royalacademy.org.uk/
http://www.tate.org.uk/
There are boat trips on the Thames inc to Greenwich where you could go to the observatory.
http://www.rog.nmm.ac.uk/
There are may cheap theatre tickets going so a night seeing a show or at the theatre is a possibility. If you wanted to go further afield Stratford upon Avon is lovely and Shakespeares birthplace where there are always productions on.