As has been said the Cheviot in isolation offers fine bog snorkelling, there are routes when it is dry that are worthwhile imho, a great longish loop that has a great feeling of being out in the wilds, riding a huge chunk of the border ridge, is to leave Wooler West of the common to follow BW up through hells glen to broadstruther all ridable, continue on the BW to the top of the hawser burn, follow the path up to Scauld hill, some carrying, now follow the Cheviot tourist route with a carry to the summit, flagstones and boardwalk onto the border ridge, follow this over the Schill, then one of the the best bits, down steer rigg all the way to green humbleton, then follow St cuthberts way off right, either follow this all the way to Wooler, or opt for the minor road (30+ miles total), would only recommend after a long dry spell.
edit. the start of the route is the one shown above to the Hawser burn