Matts suggestion is a good one if contemplating that area consider searching more info on:
Petruth paddock campsite in cheddar, walking distance to restaurants, pubs, Cheddar Gorge, working cheese factory & tour (cheese tasting) and supermarkets. Nice walks biking.
Wookie hole: ancient caves, stalactites, mites etc. Caves were used to mature Chedsar cheese, A little touristy but worth a visit.
Bristol, relatively close to Cheddar: SS Great Britain in dry dock, banksy artwork, heritage dock area, museums, check parking height restrictions in the city centre car parks, rail station car park has no height restriction but is a little more expensive. (White Hart pub is a good friendly local pub with good food at reasonable prices)
Clovelly - north Devon - Heritage site, steep cobbled street leading to fishing harbour, nice pub at the bottom of the steep street, sardine fishing community / museum preserved for future generations.
Lynton and Lydmouth (noth Devon) just outside national park area. ( area of outstanding natural beauty)
Stone henge & visitor centre (English heritage site) expensive but unique - national trust membership may worth looking into if you choose to go to other National trust sites while in U.K. ( National trust own many many heritage sites throughout U.K., check out “National Trust” website) Stone henge is not directly owned by National trust, athough national trust members, get in free when booking in advance at stone henge ( including free parking for National trust members)
Glastonbury Tor , park in town and get the tourist bus to the base of the Tor, walk the last part ( no parking anywhere near) then go and Look around Glastonbury town (spiritual touristy town)
Bath - Roman town spa and baths, accient town, (tourist area) nice architecture (ancient town)
Must have:
Cheddar cheese from cheddar
“cream tea” tea with scones, jam and clotted cream, quintessential English for the south west of England
Cornish pasty ( available outside Cornwall)
There are lots and lots of options in and around Somerset and Devon and lovely places to visit, views and beaches.
Good luck with the planning. Please ask if you want some specific info on a place or area, I’m sure many will have super advice for you to use for further research.