Darlington Council has produced a couple of cycling maps: one of Darlington and another of the Tees Valley. I’m not sure if they are free but an article in the Town Crier magazine implies it. To get a copy of The Darlington Cycle Map or Tees Valley Cycle Map call Sue Dobson on 01325 388277 or email sue.dobson (at) darlington.gov.uk.
If they’re still the same leaflets, I had a copy of the Darlington Cycle Map a few years ago, but I have no idea where it is now.
If I recall correctly, there were three rides, with varying proportions off-road. The Catkill Trail and Salter’s Circular rides are both to the north of the town, on the bridleways between Barmpton village and the motorway. The Heighington Boot is between Heighington (surprisingly) and Darlington.
I saw waymarkers for all three routes on my ride a few weeks ago, so they’re still available and rideable.