If you get an open top sightseeing bus you'll be able to get on and off the bus at the various sites around London. I think there are 3 routes to take and 2 show alot of sites and the other only shows the oyal Albert Hall. They take you past places like the Houses of Parliment, the Tower of London, near Buckingham Palace, Trafalgar Square, the Planeterium/Madame Tussads (these are next door to each other)

The London Dungeon is a place to go as well, the shopping bits Regent St, Covent Garden, Oxford St are good if you are here for a Sunday visit Camden Market its good here lots of weird and wonderfull shops/stalls and people.

You can get the underground to the sites as well as alot of them are near a tube station.

Buckingham Palace and the Tower of London are where I would go oh and Madame Tussuads. I have been to all these places and all the above to and would recommend going. The Millennuim Eye and the Millennuim Bridge are also worth taking a look at.

Leciester Square is just good for something to eat and has a few pubs too and Picadilly Circus for the pigeons and to have your picture taken underneath the advertisements! (I have one and I'm English)

Cant think of anything else, possibly the Rock Circus too, I havent been there but would like to.

And if you have time go and see a show in the West End!