Cross fell up and around clockwise to Teeshead and down past Grumply Hill. Great Dun Fell road climb, not been over the back for a while but the bridleway was steadily droping into the Tees.
High Cup Nick always worth a look, ride over to Cauldren Snout. Unfortunately you’d then be off and pushing the tarmac access road where bridleway becomes footpath. And ignoring the well constructed track that takes you from the car park to the B6277. Once you’re in Cumbria the track into bottom of the valley / Tyne Head is chewed by mx’ers. I tend to stick to the main road and blast down past the mighty Yad (yes it is a ski lift on the hillside) and take the C2C into Garrigill.
Futher E and since it’s dry Allendale and Hexhamshire common, some routes shown on the map above.
Never ventured over but Crosby Ravensworth / Crosby Garrett area has a good network of bridleways. And then there’s Bowderdale and a circuit of the Howgills.