My Wife and I did a wonderful four week road trip of England and South Wales in 2017. The largest cities that we visited were Cardiff and York. We stayed away from the London area. The British countryside is amazing. Britain is loaded with historical places as well as very scenic places.
Originally, we had planned to do Scotland as well in the four weeks, but the more planning that I did, it became apparent that we easily could skip Scotland for another trip. In planning, I picked places that were natural for tourists, as well as places that my wife and I had ancestors (from there).
My detailed story of our road trip as well as our transatlantic cruise back to the USA is accessible at this link.
28 days in Britain and Celebrity Eclipse home
https://www.cruisecritic.com/memberreviews/memberreview.cfm?EntryID=599139
Not sure how much time you plan for your road trip, but I have some tips:
1) try to limit your driving time per day to two hours.
2) try to find lodging with free parking at a small hotel or B&B that is centrally located so you can walk to key areas in the city you visit.
3) Have plenty of coins for parking and toilets.
4) Rent a vehicle that is large enough for your luggage to be placed in the trunk (boot for English). If your luggage is visible while parked, it may attract thieves that would break into your vehicle.
5) Rent a vehicle with automatic transmission and a navigation system, if you are from North America and normally drive on the right.
6) Take a good map with you as a backup.
A couple of posters advised you not to rent a car after a transatlantic flight. I agree that it wise to be cautious when driving after a long flight.
On two occasions, we rented a car after such a flight and I had no problems driving. We rented the car in the early morning and I only drove about two hours. For example, our drive from Heathrow to Bath was a little longer than two hours.
Note, that I know my own metabolism. I tend to be very excited about my trips and am ready to go after a transatlantic flight. I do get tired later in the afternoon. It is wise to be careful, but I disagree that categorically no-one should drive after such a flight.
If you are headed into an area with heavy traffic and more likely to be delayed, then perhaps it would be better not to rent after the flight. You mentioned Dover, are you planing to stay in England or cross the channel?