Buy a buss pass, it costs you 3:50 pounds per day and you can travel to EVERY zone with it
You can buy it everywhere were they sell newspapers or cigarettes. With the buss you can SEE a lot more of the town, and it's much more fun than the tube.
If you plan to go to Madame Tussaud's try to buy your ticket online, BEFORE you arrive there. It saves you at least of 1 hour queueing.
London Eye is definitely a must too. If you queue at Madame Tussaud's, you can buy tickets for London Eye and London's Dungeon there too and it saves you some money, I think 5%, so 5 pounds. They cost ya all three together cost you 50 pounds.
London's Dungeon is very cool if you are into horror stuff. Be careful not to arrive in the court and get judged
It's fun though, but in summer it can smell a bit nasty ...
The Tower of London is only cool, if you like to see the Royal jewelery, otherwise it's a rip off.
You can go to the Wimbledon museum, but it's a bit far away ... I wasn't there so I dunno if it's worth
Try to catch the change of guards at the Buckingham Palace. They are every 2nd day, so check it online at what day it will be when you are there
The park near the Buckingham Palace is also
Apart from that I guess you know already which are the usual suspects in the sightseeings (Big Ben, Picadilly Circus etc.)