Have just thought of another couple of places that you might like if you're driving - Willow Wetlands Centre and Hestercombe Gardens. A bit closer to Cheddar there's the reservoir, the woods, King John's Hunting Lodge (check opening times carefully on that one though), and Axbridge itself is a pretty (very) little town.
I live in Weston and it's not THAT bad (I've lived in plenty of worse places) but it does get very busy along the main drag of the seafront between the New Pier and the Old Pier in summer. It's nice and flat though with a good promenade for around 3 miles, and on a sunny day it's very pleasant, there are a couple of tea rooms near the old Knightstone Theatre (now flats, of course....) which are quite nice. It is the second highest tidal range in the world though (I think it's second, anyway), and when the water is in, it's IN, but when it's out, yes, it's just mud flats. For hours. And hours.
Burnham is sort of a smaller version of Weston without as many amusements, though it is a lot quieter, or if you're up to driving up the coast, Clevedon has some pretty walks.
I personally find climbing up the Tor hard work (it's 158 metres high and yes there are steps, but even some of the official sites tell you it gets steep very quickly) so hats off to the PP who didn't think it was a bit of a workout!! Also agree with the poster on Clarks Village - again, though, it's nice and flat with lots of places to sit and people watch. A lot of it depends on what you like to do, really.