Science museum is next door to the Natural History museum, then walk to the Princess Diana memorial park with the big pirate ship. If its very warm you could also go for a swim at the Lido.
Take a trip to the Olympic Park there are several big parks there, the giant slide and check what is happening at the Aquatics centre, Dd and I went when they had the giant inflatables out and it was brilliant. Then you can go shopping and to the lego store at Stratford.
Take the DLR to canary wharf and get a boat bus to cutty sark, you can visit the planetarium and Greenwich meridian line too.
Visit the tower of London, Dd loved this then walk along past the Globe to the Tate modern.
Hop on a train at Marylebone and go to the Roald Dahl museum in Great Missenden, they do the best hot chocolate and chocolate fudge cake. There are also 2 walks, one up to the church where Roald Dahl is buried and there are giant (BFG) footprints leading to his grave and a second walk which passes many of the places that inspired his books, up through a woodland where you can see red kites and the 3 farms from Fantastic Mr Fox.
Shreks adventure is good, the London Eye is OK just to say you've done it. The sea life centre is pretty much the same as any sea life centres but with more tourists stood in front of exhibits taking videos.
If you are travelling by train you can often get 241 on most attractions if you fill in the form and show your tickets.