The Forest of Bowland (Not far from the Yorkshire Dales, "next door" in fact) which was the landscape where Tolkien was inspired to write Lord of The Rings & The Hobbit etc. Its beautiful. Lake District of course as others have said.
I would 2nd Manchester as well, wouldn't bother with watching Manchester City (although it pains me to say they are the better team at the moment) only go and watch the first club in Manchester... United.
Northumberland. In parts the most rural quiet place in England I have ever been. A must would be a visit to Cragside (A National Trust Property) to look at exquisite joinery and furniture. It was the 1st place to have electrical lighting in the UK & powered by a hydroelectric dam so I remember. As well as Bamburgh Castle in Northumberland for its amazing furniture collection and top world-class joinery....never mind the castle itself!
Somerset - Glastonbury High St and it's Tor as others have said. Stonehenge in Wiltshire.
Scotland, Highlands & Islands. Edinburgh and Glasgow etc. Whisky tours, locks and ancient stone circles older than Stonehenge.
London, Cornwall, Wales
North and South and Mid Wales, magical place.
The Island of Ireland
too, only a quick 45min (if that) flight over the sea from the UK. Neolithic Burial Roundhouse Monuments older than the pyramids and Stonehenge.
Enjoy!