Like most places, Durham has its nice areas and rough areas.
Belmont has a range of local shops (butchers, greengrocers, pharmacies, bakers, Spar, Small Sainsburys). Couple of nice primary schools and a good comprehensive.
Pittington/High Pittington also lovely, great primary but lacking other amenities.
Sherburn Village (I’d personally avoid Sherburn Road, Sherburn Hill like the plague) also has pharmacy, bakers, co-op etc. Easy reach of A19 and A1.
Shadforth nice little village.
Shincliffe is really lovely and just a gorgeous stroll along the river into Durham City. If I could afford to, I’d live there. High Shincliffe also nice.
Bowburn, I have a friend lives there and the newer estates are nice but a lot of unsavory areas too.
Coxhoe has a lovely range of local shops. Sedgefield another nice place. Neville’s cross nightmare for rush hour traffic but walking distance to city. Catchment area of the sought after Durham Johnson school.
All of those villages have nice walks on the doorstep. The coastline is beautiful as is the Durham dales/Weardale. The City itself very much caters to the students. As a local, I feel DCC forget the students are not here all year round. Lots of bars, coffee shops, student accommodation. There’s a handful of small independent shops but the majority of the larger shops have moved to out of town outlets. We have great cinemas, restaurants, a lovely theatre and of course the stunning cathedral/castle.
Peterlee, Horden, Easington (Lane, Village & Colliery) are awful but you can buy a house for next to nothing… there’s a good reason for that! Ludworth, Shotton, Wingate, Haswell, Thornley, Wheatley Hill, the Trimdons, Hartlepool, Stanley, Brandon are also areas I wouldn’t consider living in.