Depends what you like doing.
Buckingham Palace from the outside
St James' Park
Tower of London
Houses of Parliament
Shopping on Oxford Street/Carnaby Street
Any museum such as Natural History, V&A, Science Museum
Gallery such as National Portrait Gallery or something at Southbank
Jump on a hop-on/hop-off bus to get an overall feel for the main centre
Nightlife is good - theatres, dinner, clubs, Soho over 6 years ago
As a theatre lover, I'd say check out the West End! There are some simply amazing musicals going on at the moment, and a few that have premiered in London before Broadway that are worth catching. The best example I can think of is probably Matilda; it's great whatever age you are and really engaging and often hillarious! It's visually amazing too - I haven't seen such a good set at a theatre in a very long time! It's on at the Cambridge Theatre right in the heart of theatreland!
Check out: http://www.cambridgetheatrelondon.org/matilda-the-musical/
I hope this helps! about 6 years ago