late august 4 day/3 night trip out of London

You can use ViaMichelin.com to get driving-time estimates for the places you hope to see.

I've been to the areas you're interested in, but I used public transportation, so I don't have a good sense of how much time you'll need to spend if you drive yourself, or how challenging the driving will be. However, this seems like a lot to try to cover in the time you have.. You say you have three nights and refer to "four days". I would say three nights is two full days plus some extra hours on the first and last days, which is a lot less than four days.

I like museums, especially art museums. Including museum time, I thought Oxford needed more than one full day and Bath, about 3/4 day. (I found Bath's architecture too samey to hold my interest, but there were two good museums.) If you don't want to do some town-to-town walking, you can see a lot of the Cotswolds in just one day. The countryside is pretty (assuming the weather is decent), but you you need to think about how many cute villages with thatched-roof cottages you need to see if you're driving between them.

As outlined in the preceding comment, it's a little unclear how much time you'll actually have outside of London. Are you leaving London on the morning of Day 1, then spending 3 nights in location(s) TBD, and returning your car in the afternoon/evening of Day 4? Does your train for Paris leave in the evening?

In any case: to get out into the countryside and have a relaxing time without constant driving, I'd choose either Bath or the Cotswolds. Bath itself is, of course, a sizeable city (around 90,000), but driving there and back would give you many opportunities to stop in small towns and perhaps take a country walk. If you take the A4, which goes through the scenic market center of Marlborough among other towns, you won't be whizzing past on the Motorway. It will be slower but more scenic. I'm not as familiar with specific driving routes in the Cotswolds, but there too you can find small-town pubs and places to walk.

Consider going by rail or bus from London to Oxford, picking up the rental there, then touring Cotswolds to Bath, dropping the car and returning to London by train.

Train or bus to Oxford from London is an hour or so. (The train station is a few blocks from the center of town.) Driving would not be faster and you'd need to find and pay for parking.

Avoid driving in London, especially if it's all new to you.

Bath-London trains terminate at Paddington Station. You'd need to get across town if you're going to Paris by rail. A cab is worth the cost. Allow 45-60 minutes for the ride, then pad it to be comfortable.

To experience the country outside of London does not mean that you're restricted to Bath, Oxford or The Cotswolds (in fact visiting Bath isn't experiencing the countryside). What are your interests in visiting those three areas (other than seemingly every American goes there when visiting England, one day I'm going to open up an afternoon tea room in The Cotswolds offering optional side trips to Bath and Stonehenge!)?

Bath is great for those interested in Regency architecture and of course the Roman Baths (which are excellent) but if neither of those interest you then I see little reason to go.

The Cotswolds are not unique in England, similarly attractive villages can be found up and down the country and without the hordes of tourists.

I've never visited Oxford (driven past plenty of times) so cannot comment on it. It doesn't really hold any particular interest for me but evidently it does for many others.

There are many, many places that will give you a countryside experience in any direction from London. What your interests are will be a huge help for those who are able to offer better suggestions.

It is important to state when you'll be leaving London (will you have the car in London or travel elsewhere to collect it?) and when you'll be leaving for Paris? It may be that you actually realistically only have two nights outside of London.

Thank you all for your advice! You are correct that we really only have two full days. We decided to get a place in Oxford and then to rent a car in Oxford instead of trying to drive out of London. It doesn't seem that we really need to go to either Bath or the Cotswolds and can explore using Oxford as a home base. Again - thanks for the advice.

With this trip - the goal is for (kids ages 11,13,16), myself and husband to see a different part of our world. My daughter is heading to college in a few years - and we thought it would be nice to see a university town. We love theater and reading and biking and walking and are thrilled when we come across some small thing that is different from what we are used to seeing.

I rented a car out of Oxford this summer, first time driving in England, and honestly it wasn’t as scary as I had been led to believe. I would suggest a gps though.
The hardest part will be parking in oxford, depending on where you will be staying. If all else fails, there is a Park and Ride outside of Oxford.
Approximately an hour and a half outside of Oxford is Lacock, which was one of my favorite stops. Avebury is between Oxford and Lacock and is worth a stop as well. Both can be done in a day.

Blenheim Palace and grounds are also a good, and easy trip out of Oxford.

I think you have a good plan. Take the train from Paddington Station to Oxford, spend a day there visiting some of the colleges and maybe a museum. There are good walking tours from the TI. Rent the car the next day and drive through some of the Cotswold villages, do some walking, return the car to Oxford and take the train back to Paddington. A taxi would be the best way to get to St. Pancras Station where the Eurostar leaves for Paris. Allow ample time for this connection, you'll need to be checked into the Eurostar well ahead of departure.

Our host's England guidebook has good suggestions for the Cotswolds but there are many options and other guidebooks may be useful too. If the car has GPS so much the better, but a good map also helps. If you can get an automatic-shift car you'll have one less mechanical variable to think about as you get used to driving on the left side. For me, the hardest part is getting into the correct lane when turning -- instinct pulls me to the right and my wife shouts "left left left!" until I get it right (that is, left). ;-)