Depends on your budget.
Country houses in the Meon Valley area can be quite expensive.
Or you can try Whiteley near Fareham. Large modern development what somehow seems chav-laden, especially the expensive houses near the golf course where loads of footballers live.
Are schools important? Like most places, houses in the catchment areas of the best schools cost 15% or so more than they might otherwise. And because of the over-development of the area, some schools are seriously over-subscribed, so kids are having to be shunted some way to the less-favoured schools (you know, the rough comps that serve the sink estates).