Where to stay in Yorkshire Dales?

It’s probably a good idea to share the places you have thought of. That way we can confirm or otherwise whether they are good choices.

One place we looked at is settle.

Also Bolton arms and Leyborn

Oops Leyburn

We stayed in Grassington the first time we went and Richmond the second time. Grassington is the town that is featured in the new All Creatures Great and Small though it is not where James Herriot lived and worked.

We loved both towns. We took a bus to get to them, and were able to do some hikes from both places. They both had a nice selection of cafes and restaurants.

By the Bolton Arms I assume you mean the Devonshire Arms at Bolton Abbey. That is a bit limiting by bus as it is only served by a 3 days a week bus between Ilkley and Grassington, the Saturday only bus Harrogate to Skipton bus, and the Embsay Steam Railway from just outside Skipton.
Leyburn is not too bad with quite a reasonable service on the Little White Bus to Hawes and Garsdale Station on the Settle/Carlisle line, also to Northallerton station (on the East Coast main line) via Bedale.

Look at www.nationaltrust.org.uk under visit for Yorkshire. They have info on touring Yorkshire Dales without a car. October has what is called "Wait a Minute Weather"...your choice of rain or showers and followed by clouds and blue sky. You are past the Autumn Equinox at a higher latitude so earlier sunsets. Wear layered clothing with a rain jacket and sturdy footwear. Plan on being checked in your stay so you can be in the local pub by dark.
We walked on Hadrian's Wall about that time of year. A military jet did a turnaround there and seemed low enough that we "saw the whites of their eyes"! They have hop on hop off buses there.

Look at HF Holidays. One of their locations is at Malham. They do 3, 4 and 7 days stays at their country house hotel. +Offer a pick-up from Skipton rail station. All meals are included and you can do guided or self guided walks.

www.hfholidays.co.uk/country-houses/locations/malham-newfield-hall?mhVisitorId=1505824529

Settle is a good choice as it is easily accessible by train and is an attractive town with plenty of facilities including places to eat.

We have spent many holidays based in Settle. Once we arrived we parked the car and didn't use it again until it was time to leave. There's plenty of scope for walking from Settle. You also have the train to palces like Horton in Ribbledsale. Ribblehead viaduct which gie easy access to Pen y Ghent or Whenside. You can also catch a bus to Skipton, Clapham (Ingleborough), Ingleton (waterfals walk) and Kirkby Lonsdale.. Malham is also walkable from Settle.

There are some ideas for walks here and here.
Call in at the Tourist Information Centre in the Town Hall when you arrive for lots of information about walks in the area and maps.