Hmm. Natural History Museum for one... London Aquarium for another.
The Science Museum's interesting too, but huge. The famous market's aren't at all what they're cracked up to be, so you'll probably not want to go there... Spitalfields market is very good though, and has a small but very good 'hand-powered complex machine' (for want of a better description) museum in the middle of it. Not sure what else really. Have a look at Buckingham Palace I suppose, but watch out for the tourists. It all depends on what sort of stuff you like.