I'm sitting at my em+pee's house in North Northumberland as I type, just Northeast of the Cheviot. I would advise bringing a singlespeed. Ark. A singlespeed ark.
If it's dried out, set off SE of Holystone and make for Simonside, it's really nice round there with some happy trails.
EDIT: And Cheviot is a horrid boggy mess – not worth it, there are far better hills to wander up, down and around in the Cheviots.