As with Noise, I may be biased. But living next to Richmond Park, Kew Gardens, and the Thames path has made us VERY happy. The kids love watching the deer, running around the soaring roofs of Kew’s Victorian greenhouses, and watching ducks and swans on the river Thames.
London has lot of parks on offer – if you have the option to live near one, I recommend you do. Have a look here:
1) Check out parks on this map by the Greater London Authority.
2) Here an article by Time Out, with a bit more description on some of the major parks.
Personally, I would also add the following for SW London:
– Kew Gardens (Kew/Richmond, SW) (not strictly a park, but a wonderful place to visit, including playgrounds. Very affordable with an annual membership.
– Bushy Park (Teddington/Hampton Wick/Hampton, SW)
– the extended greenery along the Thames from Kew and Kingston or, on the opposite side of the river, from Isleworth to Hampton Wick. This includes a number of stately homes – Syon House, Marble Hill House, and Ham House – as well as a walking path on both shores. [However, green or not green, I am not advocating for the noise in the Northern part of this lovely stretch of the Thames – it’s right on the approach to Heathrow airport.
– Wimbledon Common, across the road from Richmond Park. Lots of space, and horseriding! (also in other parks/commons)
The best of both worlds – city living with access to nature (but not quite wilderness…). Enjoy!