Well, I live in Oxford, and although I don't have children, I do work in a preschool and with local Brownies, so I'll chime in!
I would say that Oxford is a good place to have children. Where I live (a middle class victorian terraced neighbourhood) there are a lot of young families, and the local school is considered quite good. We have a lovely park with a pond, and I see lots of children cycling through the neighbourhood and playing with their parents in the park.
Of course, a lot of this experience depends on where you live, and I'd research the local primary schools to find one that fits you and your children well. The greater Oxford area is actually quite large (as villages have gotten swallowed up), and has a lot of diversity in character.
Some more points to consider:
Lots of things to see, and some very good free museums.
If you have a car, it's easy to slip out into the countryside and see the villages.
Lots of people from all over the UK and the world, as there's not just the University as a draw, but also science laboratories, etc. As a North American immigrant, I am not an oddity or curiosity, here.
Outside the city centre in nearby villages (walkable, bus, short drive) there are child-friendly pubs that have playgrounds or hire bouncy castles in the summer.
Housing is expensive here.
The shopping in town isn't considered great, for whatever reason.
London is 1 to 1.5 hours away, and a day visit is easily do-able.
I'm drawing a blank, but if you have any questions, please ask.
