We went here yesterday and had a really nice day out. This museum is in Forest Hill (just down the road from Crystal Palace). We got there at 11am (it opens at 10.30) and there was plenty of parking on side streets. The museum is free with one paying exhibit (Robot Zoo - very good interative fun for kids) and this was £5 per adult and £2.50 per child over 3. It is not a huge museum but they have some lovely things there - a big room for the natural history stuff, a free exhibition on Africa, a room full of old musical instruments from all over the world. They also have a very good medium sized aquarium in the basement which is free. The cafe is very good if a little expensive but there are 16 acres of pretty grounds to picnic in if you wish. You can easily spend a good 3-4 hours there and it doesn't get as manic as the central london museums.
www.horniman.ac.uk