Merton Park is a very lovely area (not sure what your budget is) and has some independent coffee shops etc...along and off Kingston Road - but is still probably only a fifteen minute walk into Wimbledon Town Centre.
Can't help you on the prep school front I'm afraid, but some of the state primaries in Wimbledon are very well-thought-off and sought after (Dundonald, Bishop Gilpin, Pelham, Merton Park, Wimbledon Chase, Wimbledon Park and Holy Trinity) and probably have a general intake that's socio-economically similar to the children attending the prep schools. But, and here's the caveat, you will need to really do your research about catchment areas because they are tiny and it seems that there are parts of Wimbledon, even in the central areas, which fall outwith these!
If you live in Wimbledon, secondary-school-wise, there are some fantastic grammar schools (state) for girls and boys in Sutton (Sutton Grammar, Wallington County Grammar, Wallington High, Wilson's Boys, Nonsuch High) and Kingston (The Tiffin Schools) and Ricard's Lodge and Rutlish are the state comps which are quite highly thought of these days and doing better, results and reputation-wise, year on year.
There are some excellent public schools too with probably King's College School (in Wimbledon Village) and Wimbledon High School being the most obvious. Obviously, though, with good transport links to London, Kingston and parts of Surrey, there are many others to consider too!
Good luck and let me know if you need any more info - although we are ideologically wedded to the State system, so I'm not much help with particulars about prep and public schooling!