I delayed answering, as I have just visited today! We are staying near Wells.
We parked on the road in a residential area in the village for free. The spaces in the pay car park are not generous sized. NT members do not get free parking here.
We walked the 3 mile cliff top walk loop starting at the Eidelweiss tearoom - there are several options for walks. The path is poorly sign posted, particularly on the half not owned by the NT. Getting onto the cliff top to start the walk is a scramble - the route is very steep and has loose rocks underfoot and many of the boulders have been polished by the many boots treading them over the years, so they are slick. This would be treacherous if it were to rain. Parts of the track that are bare soil were slightly sticky mud and it hasn’t rained much here this week.
There are some good views from the cliff tops across the Somerset Levels, but for most part of the walk, you cannot see the gorge. It’s a scramble down to road level, across the road then onto the NT side and another scramble up including many steep steps. The path down into the village on the NT side was the worst of the 4 ups/downs that you need to negotiate. I can certainly feel my knees now!
The village of Cheddar itself is tacky and best avoided unless you want to pay over the odds for cheese, most of which isn’t made there. We drove up the gorge, which is very winding. Whoever drives won’t be able to see much, as you will have to focus on the road and there will probably be a stream of traffic behind you.
Cheddar Gorge itself was ok, but I wouldn’t go out of my way to go back there.
I much preferred the walk that we did yesterday at Brean Down where you get great views over the channel to Wales. This has a NT car park and tea cafe.
We have also visited Lytes Cary Manor (NT) which was one of their better presented properties. Wells itself is a gem. Glastonbury is on a par with Cheddar Gorge - I won’t be returning in a hurry.
We had hiking boots on and you certainly need shoes or boots with good supports.