My information maybe outdated, as I haven't lived in York for a few years now, but still have family living there. Its an ok area as in its not bad but not a popular must have postcode area. Does that make sense?
I have friends who live off of Holgate Road and are happy enough with the schools (Primary and secondary), the children are happy.
I used to live on Heworth Green which is a main road into the city centre. Again mixed area, nice big Georgian townhouses and a few semis, but backing onto a large council estate. That is the problem in York lots of nice areas are very close to the not so nice areas. H's parents live in Clifton, which is a large area and 10-15 minute walk from city centre right near the nestle factory and the hospital, but there are several parts, the rougher council estate where they live and then the newer built Clifton moor housing estate, which is mainly privately owned.
I would say this was a better bet, close to the city centre, easily walkable. good schools and an outstanding school, also a good secondary school. although the house needs work.
or fulford is a good area, some good schools and still quite close to the city centre, just over a mile so walkable again. I have friends in fulfors to and they are happy with the schools and community . www.rightmove.co.uk/property-for-sale/property-48225701.html?premiumA=true