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.
I agree Hornimans fab I live near there and go most weekends with DD (18 months), lovely gardens, gorgeous planting, most of it is dog free so great for picnics with little ones running about safely, cafe very friendly and very baby/child friendly, a corner with animals (geese, rabbits, goats etc.), and of course then there's inside - aquarium, music room where little ones can bash away at some weird and wonderful instruments from around the globe etc. There's even a revamped playground if you cross the south circular! I could go on but suffice to say my DD loves it and it always feels like we've been on holiday when we have an afternoon there - and everything is free except Robot Zoo.
Agree with the others. We go there at least once during the half-term breaks and a handful of times during the summer hols. I didn't think much of the Robot Zoo though - we are a family of 4 and for the price we paid, it certainly wasn't worth it at all.
Across the road, there is also a playground with a couple of climbing frames and a huuuge 'sandpit' (with ropes etc for older kids to climb around on) and there's a pretty big grassy area too.
it is great there, but be warned if you go during school holiday time, especially if its a rainy day, it is often rammed - the cafe is ludicruously full - last time we tried to meet some friends there and ended up going somewhere else entirely to feed the kids, cutting our visit short due to this