Oooh yes, Wimbledon still rocks! I'm a Wimbledon-Park resident.
It's very baby/toddler friendly and you can't really go far wrong with Wimbledon Park (the actual park) with its sandpit, splash pool, play areas, tennis courts, cafe, loads of space etc. Then of course there's Cannizaro which I'm sure you know which is lovely with my little one (2.5yrs), very safe, lots to see and very peaceful. There's heaps of music groups if that's your thing but best of all I think, is the feeling of being in London but still keeping a lovely town/village, safe feel.
All the best!