Hi there! I'm just north of Newcastle city center, which I really love, though I think that's probably too far for you. I haven't spent time in many of the places you mention except for Durham, which is absolutely charming! That being said, I would choose to live in Newcastle over Durham because we don't have a car and the access to shops, entertainment, etc. available via the Metro is essential. Also there are drawbacks to living in a tourist town, which Durham is much more of than Newcastle. (Unless you count the idiots who come into Newcastle on the weekends to get plastered, but since we have a toddler we're never around that crowd!)
My friends here speak pretty poorly of Sunderland, though I can't give you any personal experience there.
As far as areas south of Newcastle, I have heard good things about Whickham and another neighborhood some friends were looking at moving to but whose name I cannot recall for the life of me! I'll post again when I figure it out.
Tynemouth is one of my favorite places to go in this area - it's so cute and right on the Metro! I have no idea what it would be like to live there (as far as schools or whatnot) but even if you don't choose to live there you definitely need to go!
Good luck with your decision!