DH is from near Alnwick, and we have spent a lot of time in Northumberland. I have compiled a list of places to visit and things to do. It is by no means exhaustive.
Towns
Morpeth, Alnwick, Hexham, Corbridge, Berwick upon Tweed, Rothbury, Warkworth
Castles
Alnwick Castle and gardens, Aydon Castle, Chillingham, Warkworth, Belsay, Bamburgh, Dunstanburgh, Lindisfarne
Stately homes
Cragside, Wallington, Seaton Delaval
Other Attractions
Holy Island, Hadrian's Wall - Housesteads, Vindolanda and Chesters, Corbridge Roman Town, Howick gardens, Woodhorn museum, Farne Islands, Grace Darling museum, Brinkburn Priory, Warkworth hermitage, Hauxley nature reserve, Kielder, Ingram Valley, Coquet Island, Coquet Valley, Ford and Etal
Beaches
Druridge bay, Alnmouth, Embleton, Seahouses, Bamburgh, Newbiggin, Cresswell, Holy Island, Cocklawburn, Beadnell, Low Newton, Longhoughton, Boulmer, Warkworth, Seaton Sluice
Children
Whitehouse farm centre, Kirkley hall zoological gardens, Heatherslaw light railway, Eshott Heugh animal park, Northumberlandia