Region Like the Cotswolds?

Provence?

Tuscany?

Normandy?

I really don't know what area can compare to the lovely Cotswolds but have you considered the area south of London? This area is convenient from LGW. You can see Chartwell, Sissinghurst, Hever Castle, Bateman Cottage and other sites. From there we headed to Highclere to tour "Downton Abbey." Chartwell, family home of Churchill, is wonderful to visit.

England abounds with areas like the Cotswolds...Dartmoor and Exmoor in Devon and Cornwall, the Yorkshire Dales, the Peak District in Derbyshire, the Lake District. All of these offer stunning views, history, quaint villages and so on. Maybe a bit wilder than the Cotswolds but certainly as equally interesting.
Some friends did a hiking holiday last year along the Border Country between Wales and England and raved about the countryside, the towns, the castles, and the B & B's they stayed at. Could easily drive it. Fly into Manchester.

Tuscany, Tuscany, Tuscany. Wonderful hilltop villages seeped in history, easy driving distances between and among them. Pick one or two bases and day trip by car. Pick a country villa or agritourismo or a nice mid-sized town with good hotel and restaurant options and easy highway connections. We stayed for 7 nights in Montecatini-Terme and day tripped to large/mid-sized cities/small towns and villages: Florence, Sienna, Lucca, Pisa, Volterra, Cortona, Pistoia, Prato, Arezzo, San Gimignano. We had dinner at a trattoria in a vineyard (3 courses, 3 wines - wonderful).

Major airports would be Milan and Rome, both <2 hrs by train, longer if you drive. Secondary airports at Pisa and Florence would be more convenient by car.

Brittany/Normandy in France

Kent/Sussex in England

Rutland in England

Istrian hill towns in Croatia.

Andalucia in Spain.

Extramadura in Spain around Merida.

Alentejo region of Portugal.

Sicily.

Our German experts often wax poetic on small-town Germany.

Lots of possibilities in northern Spain, some primarily suitable for summer travel.

Alsace, the route du vin in particular, in addition to the other suggestions

You're spoilt for choice really. These forums do tend to concentrate on the larger places but rural Europe is wonderful and full of stunning towns and villages where you can be the only tourist there.

In France, Provence, Dordogne, Brittany, Normandy

In Italy, well...almost anywhere really, but Tuscany is pretty special as is neighbouring Umbria.

In Spain, I love the area around Girona in Catalonia - mountains and Mediterranean, places like Besalu, Olot and coastal villages like Calella, Cadaques or Tossa.

The Bavarian Forest (in Bavaria) or the Mühlviertel (in Austria) north of Passau. Large hilly forests, peaks around 1000-1200 m, many cultural attractions in the towns on or near the Danube and over the border in Czechia (e.g., Cz. Krumlov and Budejovice are accessible within 30-60 min form the lovely resort of Haidmühle).

Try Burgundy. Lots of tiny medieval towns and very rural, rolling hills with trees and meadows. The closest major airport is Lyon. I flew into Paris, trained to Auxerre and picked up a car.

Bavaria, Tyrol - both near Munich for an airport

Provence?
Tuscany?
Normandy?

These are all wondedful places to see. I have been to all of them. Each has its own character, as does the Cotswolds. What they have in common are being out in the countryside.

Tuscany has Florence for its anchor, which is one of my favorite cities in Europe. Driving in Italy is a bit more of a challenge, due to aggressive Italian drivers, but not so much. If you decide to take the train, that is a good choice in Italy.

Provence is a part of France with a lot of Roman history and it is a bit like Italy, compared to the rest of France. The Rhone River makes doing a river cruise a great choice. There are many small ancient towns to see and much to enjoy. However, in my opinion, the beaches are a bit overrated.

Normandy is wonderful, the people love Americans. The Bayeux Tapestry is a must see, as are the Normandy beaches and WWII sites.

Of the three, Tuscany would take the most time to visit, followed by Provence, then Normandy.

These are all great suggestions. We just returned from Ireland and found Dalkey fascinating. It's on the end of a commuter train line that goes into the heart of Dublin so the LEAP pass works to get you into the city. And there's history going back 5,000 years or so and including Vikings. It's an affluent area with residents ranging from George Bernard Shaw to Bono and The Edge calling it home. Go inland and there are abbey ruins and stone circles.

I recommend Pomerania - a historic region divided into two parts - in Poland and Germany
https://en.wikipedia.org/wiki/Pomerania
There are many small towns and villages, lots of forests and water reservoirs:
https://en.wikipedia.org/wiki/Ueckerm%C3%BCnde_Heath
https://en.wikipedia.org/wiki/Szczecin_Lagoon
https://en.wikipedia.org/wiki/Bay_of_Pomerania
Main cities are Szczecin, Gdańsk and Gdynia
https://en.wikipedia.org/wiki/Szczecin
https://en.wikipedia.org/wiki/Gda%C5%84sk
https://en.wikipedia.org/wiki/Gdynia
but there are also a few smaller: Toruń, Koszalin, Słupsk, Chojnice, Stargard, Kołobrzeg, Świnoujście and Greifswald
https://en.wikipedia.org/wiki/Toru%C5%84
https://en.wikipedia.org/wiki/Koszalin
https://en.wikipedia.org/wiki/S%C5%82upsk
https://en.wikipedia.org/wiki/Chojnice
https://en.wikipedia.org/wiki/Stargard
https://en.wikipedia.org/wiki/Ko%C5%82obrzeg
https://en.wikipedia.org/wiki/%C5%9Awinouj%C5%9Bcie
https://en.wikipedia.org/wiki/Greifswald
Interesting towns around Szczecin area are: Police, Nowe Warpno, Ueckermünde, Pasewalk and Penkun
https://en.wikipedia.org/wiki/Police,_Poland
https://en.wikipedia.org/wiki/Nowe_Warpno
https://en.wikipedia.org/wiki/Ueckerm%C3%BCnde
https://en.wikipedia.org/wiki/Pasewalk
https://en.wikipedia.org/wiki/Penkun
The airports - in Gdańsk and Szczecin
https://en.wikipedia.org/wiki/Gda%C5%84sk_Lech_Wa%C5%82%C4%99sa_Airport
https://en.wikipedia.org/wiki/Solidarity_Szczecin%E2%80%93Goleni%C3%B3w_Airport
You can travel between these places by train
http://rozklad-pkp.pl/en
https://www.bahn.com/en/view/index.shtml

We were in Bretagne this May. Very rural - lots of cows. Nice small towns - Dinan, Quimper, Rennes. Inexpensive in many ways. We stayed in the Finisterre area - bordering the ocean. It is historic, but not in a big way, as it is mostly out of the way for the big moments of history. But we really enjoyed the area.

Are you still there, Finnlee? Or did you ask and walk off?