Basically depends on budget, we moved from north yorkshire and love it!!
We used to live in jesmond, walk into city, on metro line, shops, cafes, restaurants, swimming pool, gym, victorian houses, town moor.....BUT students galore. I couldn't live there now due to this and not being able to nip to the lovely shops without quite honestly getting in a slight rage with it all!!! But if you like this kind of vibe then it is lovely.
Heaton further out but still on metro line and easy trip into city centre, victorian houses, schools, jesmond/heaton dene, a really decent high street, very 'suburbs' feel, quieter than Jesmond, some areas slightly run down/student rented housing.
Gosforth, lovely high street, metro into town, lovely feel, cafes, a few restaurants, very professional with young family orientated, some areas close to town moor, schools, victorian and 20's 30's houses.
City centre is great, loads to do for adults and children all year round, some fantastic amenities, great feel.
Whitley bay/ tynemouth etc are about 20 minutes drive from city centre, are incredibly busy during summer which some residents find frustrating. They are lovely but too far out to have city feel or to easily go into city for evenings etc on metro. We actually live in fenham at the moment, 20 minute walk into city, on the edge of the town moor, really neighbourly, but no cafes or restaurants, and only small area of nice big houses. We just found we got a hell of alot more for our money, can walk straight out of the front door onto the moor with the dog, walk into town for activities, cinema, eating out etc.
Best to have a look around and see what you think but hope that helps x