If I love Chester and York...

[EarlofShrewsbury]

Where else might I like?

Edinburgh?

Liverpool
Cotswolds
Cardiff
London

Winchester
salisbury

Edinburgh, Durham, bath?

Bath
Lincoln

Cirencester
Wells

Oxford

Stamford & Rutland area
Ely & Cambridge
Winchester
Bury St Edmunds

Bath
Durham
Richmond
Stratford upon Avon
Edinburgh

Ludlow
Chichester
Exeter
New Forest (Lymington way)
Durham
Bath

Lavenham and Woodbridge in Suffolk for the half timbered buildings.

Lincoln maybe for a cathedral city county town.

Canterbury

I'm guessing you like them both for their medieval nature (with roman stuff too)?
Canturbury has got to be up there. Exeter and Lincoln too.
Oxford too, I guess, but it has a different vibe about it. So many lovely cities to be fair.

*Canterbury ffs

Norwich

Some of the other recommendations, like Wells and Ludlow are very nice but day trips rather than short breaks. If you get me.

Salisbury

Winchester

Cambridge for sure. I'm from there and always think it has a very similar vibe to York and Edinburgh.

Windsor
Oxford
Harrogate

Shrewsbury is very nice and lots of old stuff to see.
Liverpool is a great City break with History but from 17-1800 onwards
www.donthibernate.co.uk/liverpool/

Bath