Depends on what you like and when you will be there I guess.
If its summer, then take full advantage of the parks and walk everywhere. If its not, then use either the bus or tube network.
Main attractions would be:
Regents Street/Oxford Street
Natural History Museum
National Portrait Gallery almost 7 years ago
There are always various places to go and see and do whatever the time. In December, around London Eye there is usually big Christmas market, ice skating at National History Museum, but my favourite is Somerset House right in central London - http://www.somersethouse.org.uk - have a great time! Of course I'll have lots of Christmas shopping opportunities on Oxford/Regent Street - go and see the Christmas Lights, also check out these links.
Hope you find something to suit, it's a great city :-)) almost 7 years ago