I live in a village along the deerness valley.
There is so much variation in villages, schools etc. If planning a long term stay then I'd say be a bit more careful as some of the really good primary schools don't offer a route into a good secondary.
My children have been to/ go to a good primary which is a feeder for a good secondary so we have a secure route. Plus I love where I live and housing is not expensive.
Housing stock is another consideration though. In many of the villages it is old mining terraces or expensive new builds. A lot of villages are seeing a huge rise in new build estates but the capacity of schools, gp surgeries etc isn't always there.
Durham city and suburbs like newton hall, framwellgate moor, pity me etc offer decent housing stock, schools, walkable to the city centre.
Langley moor and meadowfield are decent too.
Other side you've got shincliffe which is nice but more expensive. Bowburn, Coxoe
Gilesgate is worth considering. Walking distance of the city centre, convenient for the A1 for you to get around to different placement schools, some decent primary schools. Bit further you've got Belmont.
Then you've got out to Ushaw Moor and further in that direction. Ushaw Moor is fairly popular with mature students etc. Lots of recent new housing attracting people. Used to be not very well considered but that's changing. Plenty of villages further out too. Just all depends on what you want to prioritise and where you will need to commute to.