Such a broad question. How long will you have in London? Do you only want to stay in London, or would you like to travel around a little bit? Do you like art, history, culture......!!
Things/places in central London would be Tower of London, Buckingham Palace, the parks - Regent, St James's' etc, shopping is a must, Soho etc.
If you want to travel around a little bit then Cambridge, Brighton, Stonehenge, Avebury woudl all be good for day trips. almost 9 years ago
If you are planning a long trip why not book to go on the london eye where you will see it all from a great height. I also can recomend afternoon tea at the ritz, its really special. Then as fortlan an mason is next door almost then go in for a nosy its a great shop. A tour on the red bus they're great because the will tell you all about the sites too. Get tickets for a west end show. Make time for shopping you will need too, i went to harrods and spent half a day there! almost 9 years ago