Alot of my friends and colleagues have moved out of oxford to purchase in Brackley. all love it but none have children yet. I visit regularly though as quite like the town.
my friends etc live in various places on the pavillions way estate / area. has a pretty good shopping area and is the location of the leisure centre.
I used to travel over from Banbury when mine were littlies to use to the toddler group /soft play in the leisure centre. it was fab, lots of clean big toys, soft play etc and a fab little cafe.
when you visit if you come in off the roundabout by tesco, then take the left after tesco, you drive onto a housing estate but at the end of that road is a fab lake and walks. the children will love feeding the ducks there. there's also some llamas to look at. there's a private children's nursery located here too - not sure of its reputation but always looks busy.
more or less opposite tesco is a soft play company. can't remember the name but is pretty good.
brackley is very community spirited and has really embraced the use of social networking. if you have a fb account - there's a brackley page which aims to provide friendships to new people to the area. can't remember the name but pages like "brackley online carboot" will be able to help you locate it.
if you are crafty in any way then "the pin money co-operative" may be for you. These are the people I know mostly and they all share their crafts, but have monthly socials, sell crafts etc. they have a fb page too.
there's also lots of community focussed events centring around the town hall. you will definately find people and get involved in the community very quickly.
I think the downsides are that shopping is limited. You will need to either go to Milton Keynes or Banbury for clothes shopping or big purchases. there's pubs but again no cinemas - my friends go to Northampton for the cinema, but then I do too as banbury only has one screen. Bicester is also close by so you have the outlet village. other downsides are no train line so its either bicester or banbury to get into london / birmingham.