Really enjoyed Bamburgh last October and have a chance to return late August and first week in September. We stayed at Victoria Hotel and ate at the Mizen. Both experiences great. Room rates seem much higher. Please suggest a B&B in town or picturesque location inland.
You might try Seahouses nearby (fishing village) or further south, Craster (handy for the ruins of Dunstanburgh Castle, home of the kipper!), Alnwick and Alnmouth further south still, (Alnwick has a wealth of attractions - Harry Potter filming location at the Castle, Gardens, Tree House, Barter Books etc., Alnmouth a small sea side town). Further north is Holy Island (Lindisfarne) which gets separated from the mainland by the tides every day. It has monastic ruins and a castle.
Recently I was quite taken by St Abbs Head (tiny fishing village) although I've never stayed there. The walk to the lighthouse was good though!
Hope you can sort something out. Northumberland and its coastline are one of England's best kept secrets!
PS. I should say that Seahouses wouldn't be my first best choice but it is near to Bamburgh.