Wales ?
 

Wales or Not? and What ?
Traveling in UK in late Sept - planning to stop in York, on to Edinburgh -
Liverpool - Bath - London -- 2 weeks - ? traveling by train - suggestions
helpful. Interested in history - museums - local foods - shops

You already have enough stops to fill more than two weeks, so I'd say not. Especially since you don't seem to know why you would want to visit Wales.

You might take a train from Liverpool to Aberystwyth.
See www.aberystwyth.org.uk/
It's a very "Welsh" town and you will hear a lot of Welsh spoken.

Aberystwyth by train from Liverpool is difficult and time consuming.

I think you are doing enough in your two weeks without adding Wales to the list. Save it for another trip, when you can spend more time exploring the country.

thanks - for the comments -