Well said, bilbo.

I thought about Conwy, too, hetismij2. I had a successful stay there using public transport (same trip as Lyme Regis), but I thought it a bit out of the way for this trip. And, of course, it is both touristy and bigger than a village.

We really need the OP's parents to tell us exactly WHY they want to stay in a village, and WHAT they plan to do there.

If the OP does manage to find this village with all the facilities, pub, shops, great transport links and a nearby castle, I may well be tempted to buy a place there and rent it out via AirBandb!

Whitby would not be a place I would choose but Gardyloo's mention of it reminded me of when we were staying at Castle Howard a couple of years ago, the nearby town of Malton may well be ideal. Half the size of Whitby, a roman/medieval small town/large village, it is full of character. a bit of a foodies centre, some Nic pubs, on the trans pennine railway line, amazing countryside. no castle but Whitby has the ruins of one that inspired Mary Shelley to write Dracula I believe. Castle Howard (of Bridgerton fame) is not really a castle but is close by.

https://www.visitmalton.com/

Bus and train station are over the river in Norton. No idea where you can get to or from from there by public transport. I visited once from York by car. It was raining - rain in Yorkshire? God's Own Country? Yes it has been known - usually when i visit, as I am always told I should have gone the week before when it was lovely weather. We didn't stay long but it looked OK. Definitely a town.

Alnmouth ticks all the boxes.

It’s a village; it has a train station; it’s north of London on the way to Edinburgh; it has nearby castles (Alnwick, Warkworth and Dunstanburgh); it has a beach, a golf course; four pubs; places to eat in the evening; easy access to the bright lights of Newcastle; buses to explore the wonderful Northumberland coast; and a selection of accommodation from a hotel to self-catering.

What’s not to like?

I too have dithered about responding but here goes - Thirsk.
I live a few miles away and it’s a non touristy, workaday market town. It won’t have an influx of summer visitors like some places mentioned. As locals we steer well clear of Whitby in August!
Mary Shelley didn’t write Dracula, it was Bram Stoker.
Thirsk has a railway station just outside town but on bus route. It’s not badly served by buses. It has supermarkets and the tiniest of old fashioned cinemas called the Ritz.
Its main claim to fame is the link to author James Herriot. It’s ‘erriot Country!
Yorkshire folk are renowned for their friendliness.
It’s surrounded by pleasant countryside but within very easy reach of both the stunning North Yorkshire Moors and the Yorkshire Dales.
Very easy to pop on a train to York, Durham etc.
However it doesn’t have a castle!

Meant to add - Thirsk is halfway to Scotland!

I do feel you have taken my posting out of context. Someone suggested that Kendel castle was just a ruin.That response was to illustrate many castles in the England are just a ruin and they are ultra touristy . However, The conversation has been moved on now. The OPs parents want a village not village and a castle.

Which is a tributary off of the topic of this thread so not sure the relevance.

Just a couple ideas from my experiences and using public transport, with places nearby to visit. Your parents will want to be comfortable popping on buses and making connections... I don't think I'd like to stay in one place for 3 weeks, but would love a 5-6 day stay in either of these places. Hopefully they find a good public transport app for England. Good luck in their planning!

CHELTENHAM for the Cotswolds. I stayed at the George Hotel (which I loved), which is just around the bend from Cheltenham's Royal Well Bus Station. The town itself has beautiful regency-era architecture, and the buses can take you to Winchcombe/Sudeley Castle, Tewkesbury/Tewkesbury Abbey, Gloucester.
BAKEWELL for the Peak District. I stayed at a B&B which is no longer open, but the town is lovely--not too large or too small. From there, buses go to Chatsworth House, Haddon Hall, Eyam (the plague village; also featured in the book 'Year of Wonders'),

Nothing wrong with Cheltenham, wouldn't mind visiting myself, except it is emphatically not a village. The town's own web site claims a population of 117,000: https://www.visitcheltenham.com/

Bakewell, however, might work. It's population seems to be under 5,000. Have to arrive by bus/coach according to this: https://en.wikivoyage.org/wiki/Bakewell#Q2462719

Bakewell in August will almost certainly be heaving. It is very popular!
It considers itself a town as well.

I was just reminded of this web site (the vloggers were part of a PBS show on Scottish trains): http://allthestations.co.uk/

They visited every station in the UK, so you could use their site to find small, unknown places with railway stations. Might take a bit of work, but may be the best option. Fun site regardless.

If in Bakewell, don't wait until you're about to hop on the bus out of town to try Bakewell pudding. We realized our mistake settling into London-bound train at Chesterfield, the enormity of missed opportunities. Sample different "original" and "best" claimants early and often.

I’m no expert on your question, but might I suggest the Rough Guide to the Cotswolds? I’m reading it for for the Oxford part, but the beginning seems to describe the kind of places you are looking for as well as the difficulties of such a trip. Would you parents be open to splitting their time among 3 villages?