Ella,
Have a look at the southern end of Greenfield Community College, talk to the farmers on the village borders, and try Thornbeck College; the Woodham Golf Club may have land that is unused, or ask about the wooded patches of farmland off the Middridge Road (
https://www.google.com/maps/place/5...5!1s0x0:0x0!7e2!8m2!3d54.6381203!4d-1.5918891). Further north, Hall Construction or Durham Animal Feeds might help.
I found this from a quick look at Google Earth (as Drex suggested); must be plenty more: a sheltered sight is needed, one that is not visible from the roads, and that is away from public rights of way. You must be able to visit early and late and access must be direct and possible in winter. Aim for a site no more than half a mile or so from the residential areas, so if the farmed crop one year is no good for bees, they can use back gardens to keep going.
Do not knock on a farm door and ask to put bees on farmland; the kind and helpful farmer may give you the most inaccessible spot that is visible from the road and in a frost or flood pocket. Check GE thoroughly, ask your friends for contacts, talk to people in pubs, and walk the likely routes to find out if the map matches the reality; having chosen
your spot on the farm, knock on the door. If you locate a site by spring, you'll have done well; if you're offered several sites, don't accept just one: you may need the other to expand or because the first turned out to be problematic.
Allotments these days are tricky, and some won't allow inexperienced beekeepers on site (Aberdeen are the latest, I read somewhere) and as swarming and stinging may occur, they are not the easy answer for a beginner. Wherever you go, please keep two (not one) colonies as a minimum, keep bees that are a pleasure to work, and have your swarm preps memorised and the kit ready.
