In reply to DaveHK:
If Barrowburn past Alwinton is open then I'd recommend there for a very back to basics approach. It got some lovely moorland/fell running but can be super bleak if the weather is in. The Cheviots are good if boggy running.
Further south, Rothbury has Simonside crags for running and climbing, you could also get to Thrunton to run/climb/mountain bike.
There's a site right on the coast by Bamburgh which has always looked gorgeous, not too far from Bowden and the sandstone crags that way, but again if the weather is in the north east coast will be bleak (and amazing and beautiful and wonderous).
Essentially come to Northumberland, it's amazing. I love it and it deserves much more popularity, but I'm glad it doesn't get it.
Edit: just be aware of current restrictions which if you are solo won't really make any difference!
Post edited at 20:57