Chester to Broadway to Barnard Castle

We are going on a short tour starting next week and three of the stops are those in the title. I don't know the English / Welsh border area very well and I've never been to the Cotswolds, so I was wondering if anyone has any advice to offer as to the most pleasant routes to follow. I'm not bothered about going by the quickest or shortest route but I would like to enjoy the journey and so I'd rather avoid all the hassle of the M6 and M5. All advice will be gratefully received from those who know those areas, thanks.

Ally