DH is from near Rothbury and I know the area pretty well. I have compiled a list that I have saved because there are often requests for recommendations from mumsnetters, so here you are:
Towns
Alnwick, Amble, Berwick upon Tweed, Corbridge, Hexham, Morpeth, Rothbury, Warkworth
Castles
Alnwick Castle and gardens, Aydon Castle, Belsay, Bamburgh, Chillingham, Dunstanburgh, Lindisfarne, Warkworth
Stately homes
Cragside, Seaton Delaval, Wallington – all NT
Other Attractions
Brinkburn Priory, Coquet Island, Coquet Valley, Corbridge Roman Town, Farne Islands, Grace Darling museum, Hadrian's Wall - Chesters, Housesteads and Vindolanda, Ford and Etal, Hauxley nature reserve, Heatherslaw Light Railway, Holy Island, Howick gardens, Ingram Valley, Kielder, Warkworth Hermitage, Woodhorn museum
Beaches
Alnmouth, Bamburgh, Beadnell, Boulmer, Cocklawburn, Cresswell, Druridge Bay, Embleton, Holy Island, Low Newton, Longhoughton, Newbiggin, Seahouses, Seaton Sluice, Warkworth,
Children
Northumberland Country Zoo, Northumberlandia, Whitehouse farm centre
Places to eat
Ephesus, Morpeth
Nadon Thai, Morpeth
Tandoor Mahal, Morpeth
Lal Khazana, Shilbottle
Cook and Barker Inn, Newton on the Moor
The Running Fox, Felton and Longframlingtom
The Village Inn, Longframlimgtom
The Lord Crewe Arms, Blanchland
Also, if you like walking, I really recommend Simonside near Rothbury. The views from the top are stunning.