I've skimmed the replies you have received. Most stress what I might call the dramtic landscape. Some say the UK doesn't approach the photographic possibilities of the US. Maybe I have a different take on this. I view much of the English countryside as a living museum; a lot of the old is preserved, with much that is modern out of view. The very green rolling hillsides, dotted with small farms, are spectacular in their own way. Little, actually tiny, country roads are superb for viewing. Stay off the highways unless you are going a long distance. Turner,a famous landscape painter, trod these rolling hills and valleys and I doubt he was ever at a loss for inspiration. The villages of the English countryside are not to be missed. If one dosen't find them photogenic and nostalgic it is the imagination that need calibrating. Oh, and then there are the gardens - everywhere.
A couple of specific suggestions are the Cotswold and Cornwall villages and surrounding countryside. These are separated geographically, but nothing an American driver can't reach in a day.
If any of this interests you, you need to do some research. Go beyond the Fodor-style guides. BTW walking the English countryside is a great pleasure, if you are so inclined. There are many walking paths of incredible beauty that are hundreds of years old. In planning your trip of two weeks, keep the weather firmly in mind. For example, summer in the Cotswold is not as rainy as many other parts. A week of rain could really (dare I say) dampne things.