Rothbury – famous for the Raul Moat three day water pipe stake out a few years back
I would suggest coquetdale and Ingram valley (linhope spout at the top of Ingram valley). Grandparents used to farm in both those valleys for years and spent a lot of time up there, fantastic landscape and probably the most remote you can get in England.
i would also say walk from craster to dunstandborough is great,get yourself some skippers at craster?
Chillingworth castle is great and if you go to Alnwick castle you have the gardens with a great entrance building and then also the huge tree house which is worth a look!
Fish and Chips in seahouses or bamburgh,bamburgh castle is probably most impressive I think, especially with the way it sits on its huge podium of rock.