In reply to Yrmenlaf:
Surprised no-one has mentioned Causey Quarry, between Sunniside and Stanley, about 8 miles from Newcastle.
It's got to be a lot closer to Durham than most of the places mentioned so far, and is a 5 minute walk in from the car park.
It does tend to be a bit thuggy, with little below VS, but is liberally endowed with trees at the top, and has a long history of top roping.
The Low level girdle is worthwhile and certainly builds up forearm strength quickly.
It has been done wearing wellies in the wet in the middle of winter, when the ground was covered in snow! (using feet is an added luxury)
It used to be in the Northumberland guide, but I believe it has now migrated to the North East England guide -- check the database for further details.
Climbed my first VS, HVS and E1 there, although all were graded northumberland VS at the time.