These destinations are difficult to get to by public transport, are they worth the effort? If I can only visit one of these places, which do you recommend?
Cheddar Gorge and its caves are interesting, but to be really honest I have seen better caves here in Australia. No doubt you have more interesting ones in North America as well. Wells Cathedral though is definitely worthwhile. The front of the cathedral is covered in statues. The interior is also beautiful. I got to both of these places by car, so I don't know how to get there by public transport.
We too enjoyed Wells but we got there by car.
We stayed at Canon Grange B& B - I think you
must have a car
We have visited all three (with a car, however). Cheddar Gorge--we enjoyed Wookey Hole. It may be touristy, but the cave is spectacular. Wells is a lovely town and one of the best cathedrals in England. If you go there, be sure you walk all the way around the outside of the cathedral. Halfway down one side ( opposite side from the Bishop's Palace) is a complete street of medieval era homes. If you are into King Arthur, Glastonbury is superb for its associations with the legend, for a spectacular ruined abbey, and for the Tor. Also nearby is Cadbury Hill. You should visit all of these sites---rent a car and enjoy.
I like both Wells and Glastonbury. Wells Cathedral is stunning as is Glastonbury Abbey. I also like walking around the strange shops in Glastonbury. The Abbey Tea Room also has the best puddings ever.
I used to live in this area and it only takes about 20 minutes on the bus to go between the two.