Great question Barb!
The western Cotswolds, in a line from Chipping Campden to Broadway to Winchcombe to Painswick to Minchinhampton is more hilly because it is along the Cotswold Escarpment. Once you get as far east as Stow, it is flatter - gently rolling hills. Like the difference in Italy between Chianti (hilly) and the Val d'Orcia (more open with rolling hills). Both areas are beautiful and full of pretty villages.
Avoid Bourton-upon-the-Water - a major tourist town with attractions for kids and a huge parking lot for tour buses. Maybe also avoid the more southern Cotswolds, south of Tetbury, just because it is so far from the main part of the Cotswolds. And avoid the Cotswold Lakes south of Cirencester (very flat, full of gravel pits that are now lakes - some of it is an upscale holiday home area).
I would probably also avoid the south-east corner, east of Cirencester, near Bibury. You will want to visit Bibury, but this corner of the Cotswolds seems a little more "posh country weekend house" than the rest.
So that leaves you with the north Cotswolds. Burford, Chipping Norton, Stow, Moreton, Chipping Campden, Broadway, Winchcombe. Any of those towns or villages nearby would be good. And the south west Cotswolds - Painswick, Minch, Tetbury. I would recommend the north Cotswolds for a first visit. The main gardens are up there, you can get to Warwick Castle easier.
You have three choices on type of location:
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In a market town, like Chipping Campden, Broadway, Burford, Winchcombe, Stow, Moreton, Painswick, Minchinhampton. These are small towns, population about 5,000 I think? With restaurants, tea rooms and pubs. They are all popular with tourists - so they will be busy.
<< We stayed in Broadway at
Broadway Manor Cottages. They are on the outskirts of town, so it is a half mile walk on a footpath into town. These are great cottages and the only downside is that they are not historic. I think they were built in the 70s.
<< We also once stayed in Winchcombe at the Sudley House cottages - great location but the cottages were dreadful (and we were there for a month).
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In a village. These usually don't have a shop or restaurants, but will have a pub.
<< We have stayed in several villages because this is where you find a lot of vacation rentals. We stayed in Blockley (near Chipping Campden), Windrush (near Burford), Fulbrook (near Burford), Naunton (near Stow).
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On a farm or a house in a very rural location. You can walk out on footpaths, but there will be no shops or pubs nearby.
<< Our first long visit to the Cotswolds we stayed in a cottage on an estate a mile from Painswick. It did not feel really rural because we were close to a lot of places.
I think you should look for a market town or a village, because I think you will like being around people and being able to walk to shops etc.
I am happy to look at any links for vacation rentals that you find and tell you if it is a good location. I worked my way through several locations in our years of traveling here, and we enjoyed all of them - except maybe for Windrush. It is one of those villages that are mostly second homes, so it was very quiet. But it has a beautiful church with a Norman door.
Photo of Norman door in Windrush.