Avoid the towns like Fenton, Longton, Hanley, Cobridge, Bentilee, Meir, Tunstall. I lived in Stoke on Trent for 30 years and my parents still live in Stoke on Trent but a more desirable area than the areas listed above. The best areas are:-
Trentham - great location and people of Trentham like to say there are part of Newcastle and not Stoke on Trent but they are under Stoke Council.
Milton - Nice little village a few miles from Hanley, has primary school and nearby high schools, has shops galore in the little high street
Baddeley Green - Just up the road from Milton, also has some good schools nearby
Stockton Brook - Few miles from Milton and you would then be in between Hanley and Leek
Norton and Norton Green - Good schools and local shops in the vicinity
Brown Edge - More rural village, shops, school and nice pubs - close to Leek
Endon - is more upmarket village and where I lived for some time- few shops, pubs and good schools inc high school
Hope this helps!