Northumberland is a huge county with quite distinct types of scenery. Fortunately it is largerly empty away from the coast so light pollution is rarely an issue. The dark sky park is around kielder forest which is as you might imagine, full of trees but there are rolling hills clear of the tree line and the resevoir. Several superb locations up the coast as well including Dunstanbugh, Bamburgh and Lindisfarne. Hadrian's wall has a few great spots on it including sycamore gap and Steel Rigg. All of these would provide great foregrounds for starry landscapes.
The castles are accessible to get to with some caveats. Lindisfarne is subject to tides so you'd probably be best planning a top over there if you want to shoot it at night. Bamburgh is easy to get to from all angles. Dunstanbugh Castle is a little more of a trek from any direction.
Kielder is easy to get around.
Hadrians wall has several visitor car parks along it but not necessarily great photo locations. Sycamore gap is a 10 minute walk from the road along an easy track though. The most popular shooting spot on the wall at Steel Rigg is a 15-20 minute hike up the hill from the road. It's easy going though.