As a long time UK resident (ie all my life), and a confirmed Northener, I can recommend:
* York - especially the Minster (voted one of the 7 architectural wonders of the UK). Good 'ghost tours' too. Roman walls, and a small castle. Visit the 'York Dungeon' if your stomach's up to it.
* North Wales - the best castles in the UK because Cromwell didn't destroy them. Caernarfon (sp?) and Conwy are possibly the best - Conwy is a brilliant example of a medieval village that's grown near a large castle. Warwick castle is good too.
* Hadrian's Wall. The wall is amazing, the forts are mostly wall lines on the ground, but still fascinating.
* Tintagel is worth the effort if you visit the Westcountry. 'Merlin's Cave' is simply amazing.... When you're passing through Somerset, don't forget to visit Glastonbury and Wookie Hole.
* The Peak District, for some very nice scenery and great caves (Castleton).
* Cumbria - just because

Pavey Ark (Langdale) always reminds me of the back door to Moria !
* Scotland - the further north the better. Avoid men kin kilts playing bagpipes - such things are for chulrlish tourists. Loch Ness and Castle Urqhart are worth it. Glen Affric is superb. Glencoe is outofthisworld.
* Cambridge. Great city. There's a reconstructed Saxon settlement somewhere near there too.
There's so much to do and see here. I've spent 30 years doing it and still haven't seen half of it !!