Battersea Power Station. One of my favorites buildings in London. It is not particularly beautiful but it represents lots of things, at least for me. It is an incredibly big building that used to supply electricity 40 years ago. It got shut down and now it is just a massive empty shell. Pink Floyd used it in their album Animals to film a video of an inflatable pig flying over the 4 chimneys.

See a film (or even two) in the iMax cinema in the Science Museum. Huge screen and sort of cute, interesting films to watch. You may end up with a headache with all the 3D effects.

Battersea Dogs and Cats Home. A sad place in itself as there are plenty of stray animals waiting to be adopted. The cage sizes are ok, but still the animals become very stressed and some of them are quite scary.

Battersea Park. A quiet park to relax in and stroll around as it is not a touristy spot. Has some cool fountains and there is a nice path along the river.

Battersea Park Children's Zoo. Right in the heart of Battersea Park, they hold an egg treasure hunt over Easter. It hasn't got a massive display of exotic animals but it is well worth seeing as it is not too big and has enough variety to spend an afternoon.