I've recommended the Science Museum many times, on AB, for families visiting London. Despite this, I'm still a little doubtful that a child who's only just 2 will enjoy it much.
The youngest age group that the museum 'officially' caters for is 3-to-6 year olds with the interactive area called 'The Garden':
http://www.sciencemuseum.org.uk/galleryguide/EB120.asp
However, the Science Museum (like all major museums in London) is free, so you it won't cost you anything to take a look to see if there's anything of interest.
Quizzywig's suggestion of the moving, roaring dinosaurs in the (free) Natural History Museum is an excellent one. To find them, just seek out the dinosaurs' exhibition and then go straight to the very far end of the gallery. (Just look for the queue!).
Assuming good weather, a nice relaxing place (but with some fun things to do) is Battersea Park. There are trains every few minutes from Victoria which take you over the Thames to Battersea Park Station. (It's just one stop. Blink and you're there!). Take some bread to feed the ducks, then take a rowing boat out on the lake. Afterwards watch the fountain displays before visiting the children's zoo. Everything's either free or cheap. The park is a great favourite with Londoners (both adults and children alike) but is unknown to many tourists:
http://www.wandsworth.gov.uk/Home/EnvironmentandTranspor t/Parks/Parkscommons/bpark.htm
Chris