I replied to your other thread, but here is the same list that I posted there. DH is from Northumberland, and we spend a lot of time there.
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, 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, 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
As you aren't far from County Durham I would agree that Beamish is definitely worth a visit, as is High Force waterfall and of course, Durham itself.