I Went to the Horniman Museum at the weekend and it is now my favourite London museum!
The Natural History exhibits are in a wonderfully dark room, all incased in dark wood, glass sided cases
which suit perfectly the slightly creepy animals on display. Elsewhere there's an exhaustive selection of musical instruments, anthropological collections from around the world and even an aquarium!
Outside are some very nice gardens wander around and they had some music on at the bandstand when I was there (I didn't stay to listen, the description was: folk mixed with world music and electronica which screams FUSION. Shudder.) It's in South East London so now you have a reason to visit South East London.