Agree with Shropshire and Herefordshire. There's a campsite on the banks of the Wye we love. There's plenty to do in the area, NT (particularly Brockhampton, although that's actually in Worcestershire - a beautiful 'secret' valley with a medieval Manor, a place to live and die in), Hay for the bookshops, Hereford and the cathedral, Ludlow. But it's the landscape and the walking, and the times we've found a quiet place by a river and just spent the day reading, drawing, drinking tea and watching kingfishers.
Yorkshire Wolds, pretty villages and a deserted medieval village.
The coast north of Newcastle, from Tynemouth to Berwick although sadly this is becoming more popular. Also inland Northumberland - there are lanes leading up into the Cheviots which follow rivers, Ford and Etal are pretty villages.
Eden Valley in Cumbria - much quieter than the Lakes.
Dumfries and Galloway - fantastic coastline - Portpatrick is like a Cornish fishing village. You can see Ireland, Isle of Man and the Lake District from the Rhins on a clear day.
Scottish Borders - more castles than you can poke a stick at and miles of glorious, empty countryside.
Cheshire - quintessential English countryside, pretty villages, nice pubs, canal paths.