There are just so many things that you could do that this space is really not enough here.

If you like the theatre, you can range from wonderful live performances of Shakespeare at the London Globe Theatre (open air!) or the National Theatre or perhaps one of the big shows. Check out: http://www.londontheatre.co.uk/

If you enjoy good food, there are literally thousands of excellent restaurants, of course, it all depends on what you like.

If you like museums, you could try the National History Museum, which is a true joy, especially with kids. How about the Tate Gallery or the Tate Modern, if you like wonderful art.

You could take a trip on the London Eye, the great BIG Wheel next to the London Museum, across the road from the Houses of Parliament. If you like that type of thing, you could also visit St. Pauls Cathedral (the magnificent Dome is amazing) or Westminster Abbey, to visit the resting of place of so many famous Britons.

Enjoy your time and ask more specific questions if we can help.

 London is a treasure chest of things to do, and has something for every age group, and every taste.
You should certainly do the very normal things first like,
Buckingham Palace and the changing of the guard.. The Tower of London and the Beefeaters, Big Ben ,London Bridge, Trafalgar Square. Harrods, The Portrait Gallery, just to get a feel of the atmosphere, that all tourists must experience at least once.
Then you could go to Richmond Deer Park, Kew Gardens is fabulous, and great for walks and the huge tropical greenhouse and mass tulip displays, and the bluebell meadows.St James Park for a stroll. St Pauls Cathedral.
You could go on a boat trip on the Thames and have lunch or drinks and see the sights on the way, Parliment house , the bridges etc. Then you could explore Nottinghill with its great shops, or go to one of the street markets which are all over London. Covent garden is a great area to explore, as is the wax museum, and the London Eye.
From up there you can really see how London is set out ,on the Thames. Hampton Court ,just out of London gives you an insiders view of royalty.
There is so much to do and see, you won't possibly be able to see it all. Enjoy it