Echo Lucysmum (again!) on Hursley, Twyford and Itchen Abbas. Owslebury is also nice, 'tho further away. Hursley is dominated by IBM and the village is rather bisected by the main road. Twyford has the big prep school as well as its own excellent primary school and lively toddler groups and preschool. Oh, and a post office. Colden Common, South Wonston etc are rather more souless, I feel: lots of new developments and not a colossal amount of village feel about it. Sparsholt is also a proper village with primary school and active church, post office, etc, and excellent pub in the Plough.
There is apparently a shortage of family houses on the market at the moment. Some friends of ours rented for over a year before the right house in the right area came along. Fulflood and Hyde seem to be the holy grail for London emigres, with prices to match. Depends what you are looking for and what your budget is. You will always get more house for your money in the villages, with Hyde, Fulflood, St Cross and Oram's Arbor fetching the premium prices. Alresford is a lovely small town/ large village: bigger than a village, but a self contained town with lots of independent shops, a small library, its own secondary school, etc. It's close enough to Winch for its residents to use it regularly, but with a clear identity of its own.
In reality the city is small enough for villagers to dip in and out of city life as much as they do village life. As an example, NCT organises on a Winchester basis, as do other joining organisations. Do try and get hold of the Hampshire Chronicle (out on Thursdays) which has a beautifully Ambridge-esque round up of what is happening in the villages each week from their own correspondents.