most areas are nice and safe, though historical reputation sometimes gets in the way so I would suggest you probably don't want to be looking at Blackbird Leys, rose hill or Barton. But all these areas have childrens centres and are a great resource for young families :)
do you want to be walking distance from shops and parks??
Cowley has the biggest shopping centre - Templer Square outside of the city centre so being close by means you won't actually need to use the city for shopping unless you want Marks and Spencer or debenhams.
If you stay within the ring road then there are some nice estates on and around Holloway or nearer to Headington around South Park or the otherside of Cowley retail park near Florence Park.
I think your biggest problem will be students .... there is a lot of let properties and it can be difficult to find something to rent because all the students are wanting these too. similarly to buy...there's competition with the buy to let market too.
if you are happy to live outside the ringroad and rely on bus services then areas like Old Marston or Risinghurst might interest you.
As you are talking nursery school..I take it you don't need it till your child is 3 and using their free hours. if that's the case I wouldn't worry too much about this just yet, you can find an area you are happy with, settle, make friends etc then find this. Given that transport links are very good, lots of nursery schools would be available to you and you've got two years to find the right nursery.