As DH is from Northumberland, and DD is in Newcastle we spend a lot of time there. I have compiled a list of places to visit because this question comes up a lot on MN.
Northumberland Attractions
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
Places to eat:
Lal Khazana in Shilbottle
Ephesus in Morpeth
The Cook and Barker in Newton on the Moor
The Running Fox in Felton
Barluga in Morpeth - I haven't been in the one in Newcastle
Scotts of Alnmouth
Most of the pubs in the area do good food as well, but the above places are the ones that spring immediately to mind. We are just beginning to get to know Newcastle as DD has only just moved there.
Have a great week. We love Northumberland.