Thank you all for the very helpful input...great ideas and, as noted, a very interesting discussion.
The north and Scotland are all interesting, but are going to have to await a future and longer trip.
Cornwall (and parts of Devon, I presume) sounds and looks very interesting. We're not necessarily interested in additional city sites...London will definitely serve that purpose. Some of the historical sites and the historic fishing villages sound interesting. It would also enable us to stop at Wells and Glastonbury.
I keep getting a variety of input about Oxford, including in this post. I hear the architecture and history are wonderful...but there's always the caveat about the large crowds of students and bikes. We would not drive in Oxford, aside from driving out of and back to the train station area with the rental car. The nice thing about Oxford to me, as a novice of the area, were the sites sufficient for an overnight, as well as the variety of transit options to Heathrow (Oxford Express, National Coach and train). The other thought is to not stay in Oxford at all, but perhaps in nearby towns, such as Witney or even Burford on the last night adn merely drive in the final morning to drop the car and pick up the airport transportation.
The other thought, based on a friend's comment, is to drive to Windsor for the last night. He said it's got great sites, obviously, and slows down quite a bit late afternoon after the tour buses leave. From there it's an easy drive the next day to LHR to drop the car.
All very interesting thoughts...including the Cornwall option. We have some thinking to do. any additional thoughts/ideas are welcomed. Thank you very much for the very helpful input.