Many thanks to everyone who responded to my question. This helps a lot. I would like to do the Cotswold Villages by Becky tour after reading about. We would have a problem doing this entirely on our own as we cannot drive in England; I do not feel confident enough to drive on the left in a car where the driver sits on the right and shifts with his/her left hand. That's presents too many chances of a calamity.
Thus, we'd have to have an alternative way to travel from one village to the other, but would like to cover as many as possible in a day or two without feeling rushed.
I'm really not sure, but I think some of these villages are used as settings for "Midsomer Murders", or are similar to the villages where that show is filmed. Not that we really need to go to film locations at all, but one of the things that attracted us to these villages are the settings of that show.
I also would like to visit and tour Oxford.
We took the train to Bath last time and loved the town. We ran out of time before we were able to visit Stonehenge and the surrounding ancient ruins, but I would really like to do that as well. I understand that visitors are no longer allowed to actually walk among the stones at Stonehenge, although I've heard there are special night time tours that do permit that.
Bath might be a great central location for us to stay in and then take day trips to these other areas.