Walking in the Cotswolds: local recommendations?

My wife and I are planning a mid-July walking holiday in the Cotswolds and putting together an itinerary. It's our first time in this area but no strangers to full day outings (we've walked the Spanish Camino), looking to do 8-15k miles / day.

Staying 2 nights in each:

• Charingworth (Hyll)
• Northleach
• Coln Saint Aldwyns

Was wondering if anyone had recommendations of walks / areas to check out while we are there. We're not big on kitsch or "must-do" touristy things, more just looking to enjoy some tranquil scenery (and a pint). Anything welcome.

Cheers!