Another vote for Northumberland.
Bamburgh Castle is the iconic picture that appears on all the tourist literature, but is definitely NOT a tourist trap. It is well worth a visit with a lot of history attached. Bamburgh also has links to Grace Darling - if you've not read about her, then do check out her story. She is buried in Bamburgh Churchyard (you can't miss her tomb as it is the biggest ) and there is also a very interesting museum about her in the village.
Northumberland has the lot from wonderful long sandy beaches to the tidal island of Lindisfarne (the centre of early Christianity) as well as the Farne Islands ( do a boat trip frrom Seahouses). There are ruined castles - Dunstanburgh is a wonderful walk along the shore from Craster and Warkworth is super too. If you have chance, visit the Hermitage whicjh is included in the cost of the ticket and reached by boat across the river...
Cragside, the home of wealthy industrialist William Armstrong is often described as the house where modern living began. He genenerated electricity in the grounds using water power and this was used not only to light the house but for all sorts of time saving equipment in the kitchens. It is surrounded by wonderful grounds and gardens.
I've also hearrd that Howick Hall Gardens are very good, although I've not visited them.
There is Berwick, with its Elizabethan town walls.
Alnwick Castle is the home of the Duke and Duchess of Northumberland and is well worth going round. The gardens designed by the Duchess are regarded as one of the best modern gardens in the world. The Castle also featured in the Harry Potter films. Barter Books in the old station buildings is the largest second hand book shop and very popular with visitors.
You also have the Cheviot with lots of walking, especially up the Coquet Valley
And then of course there is Hadrian's Wall with all the Roman stuff...
And I've hardly scrathed the surface. (Belsay Hall, Brinkburn Priory, Chillimgham castle - decidedly quirky, Wallington Hall, Norham Castle, Hexham Abbey with its crypt, as well as ruined peles and some small villages to explore like Wooler, Corbridge, Hexham...)
Northumberland is a place visitors rush through on their way to Scotland. Foreign visitors are only just discovering what we have known for a long time - it is one of the best places in the country to go on holiday. The locals are deliughtful too and so warm and welcoming.