Upon arrival on July 3, we will rent a car at Heathrow and drive to our home base. We want to take day trips to SW England, Wales and Cotswolds. What would be a good town to stay in?
Bath would be a pretty good option, and it's a wonderful town. Of course it depends on how far you want to go into these destinations and how much driving you are willing to do. I'd be inclined to stay in more than one place.
What sort of place do you see yourself enjoying? A larger city or a small town? Based on the geography of the places you’re interested in I’d say somewhere near Bristol would be good because it’s roughly equidistant from the Cotswolds, Wales and the further South West regions such as Devon and Dorset.
Have you hired a car yet? If you stay in a place like Bristol (as Helen mentioned), Bath, Cardiff, or another larger city, I doubt you'll need one, and it may be more convenient not to have one if you plan to travel into Devon and Cornwall. In July the roads will be busy with holidaymakers.
Organised tours of the Cotswolds are abundant, and Bath is the start of the Cotswold Way if you fancy enjoying the landscape by foot.
Years ago we used Bath as a base for 5 days. While it worked as a base we spent a lot of time driving back to it from the places we took day trips to. On subsequent trips we’ve opted to stay closer to the places we wanted to visit. It just means more hotels for fewer days at each.