Wimbledon Common is brilliant. There's big grass areas for picnics and sports and that. There's also lots of woodland and scrubland to make it all feel a bit more natural and to give the birds and little creatures somewhere to call home.
The Windmill Museum is cool and there's rugby and football pitches as well as horse riding facilities. It's also a relatively nice (and cheap) place to sit and get drunk after watching the tennis all day.