It's been some years since I spent much time in the area, but I might suggest looking at Bamburgh (maybe the Victoria Hotel?) as a base. The castle is very impressive, it's equidistant from Alnwick and Berwick, close to the Holy Isle causeway, and also close for a forays to Wooler and Etal, a pleasant town and a pretty village respectively. (The Black Bull in Etal is Northumberland's only thatched pub, and not a bad one.)

Maybe do an openjaw? Into NCL, out of EDI? That way you could spend some hours going over the Lammermuirs and through East Lothian on your way to Edinburgh. (Visit Gifford and Haddington, lovely...)