The place doesn't look like "Zone 3 museum" at all. Occupying several buildings of very different styles, it is surrounded by gardens sporting a great view on London skyline - not only the Shard and Gherkin, but other less taller buildings are visible as well as the the museum is situated on the top of the Forest Hill.
Inside there is a decent collection of stuffed animals, the African hall and the Aquarium where I haven't been. The most amusing though is the collection of musical instruments thanks to the thought-through interior and lighting making brass to sparkle and wood to glow.
Definitely one of the best locations for sketching I have visited in a while.