Hi from a Yorkshire resident, but one who is very familiar with Newcastle. It's a great city, just be prepared for those cold North Sea winds!!!
As for places to live, well, I think you need to decide whether you want urban, suburban or rural. Newcastle/Gateshead is urban, can be 'gritty', but lots of great shopping, museums, restaurants etc ... good but expensive areas are
The Quays/Quayside around the Tyne Bridge,
Jesmond (inner Victorian suburb on the metro - quite chi chi), and
Gosforth (bit further out, more spacious and family oriented). On the Gateshead side,
Whickham and
Ryton are nice suburbs that have grown up around an old village centre, so they have some character and local shops - but you'll need to travel to get to any major shopping/restaurants etc ...
A bit further out in the Tyne Valley are the villages of
Corbridge, Wylam and Riding Mill - all on the train line from Hexham to Newcastle.
If I were you, I'd take a look at these types of area:
1) Urban Newcastle (City Centre, Jesmond, Gosforth)
2) Suburban Gateshead (Whickham and Ryton)
3) Tyne Valley villages (Wylam, Corbridge, Riding Mill)
4) Country Market Town (Hexham)
Try these websites:
www.gateshead.gov.ukwww.tynedale.gov.ukwww.newcastle.gov.ukHappy hunting!