I'm back with my list. It is by no means comprehensive, but a guide:
Towns
Morpeth, Alnwick, Hexham, Corbridge, Berwick upon Tweed
Castles
Alnwick castle and gardens, Aydon Castle, Chillingham, Warkworth, Belsay, Bamburgh, Dunstanburgh, Lindisfarne
Stately homes
Cragside, Wallington, Seaton Delaval, Belsay Hall & Castle
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
Beaches
Druridge bay, Alnmouth, Embleton
Children
Whitehouse farm centre, Kirkley hall zoological gardens, Heatherslaw light railway, Eshott Heugh animal park