Well, I like it. There are lots of things to do with small children and the buses are good. There are plenty of shops, banks etc and a lovely big park on your doorstep. It's also not too far from the edge of town, so it's easy to get out.
Oxford city centre is not a pleasant place to go with small children, with narrow, busy pavements and cramped shops. My friends and I only brave it with little kids when we absolutely have to. Everybody I know prefers the shopping districts in Headington, Cowley or Summertown and goes farther afield to other towns (Abingdon or Bicester, say) for those hard-to-find items. I quite like the town centre on my own or with older children, but not with little ones!
There is a scramble to get into schools, with some people initially being allocated schools which are unreasonably far away, but if you are willing and able to sit tight then places do free up because people move around so much. A number of people I know were on the verge of keeping their kids at nursery or home for part of the Reception year while sitting on waiting lists, but all did get offered reasonable schools before September.
In Headington your school choices are wider if you drive since you can consider village schools too. I realised that if I wasn't going to send my dd to either of the closest two schools then I may as well take her to a village six miles away; that was quicker than going by foot or bus/car for a mile or two through heavy traffic to another city school.
There are several highly regarded private schools if you are planning on that.
With several hospitals and a university, Headington has a very mobile population, which I find means that people are quite friendly. On the other hand, it means that you do have to keep making new friends as the old ones move away.
I can't advise on availability and price of property of the type you are after, as my friends and I are on smaller budgets. However, be aware that estate agents like to mislead people by using the word "Headington" to encompass a very large area, some of which you may find less desirable. You'll need to have a good look round to decide exactly where is acceptable to you so as not to have your time wasted when looking at houses.