Im probably biased having spent quite a bit of time there, but I quite like Crosscombe (and Correges Cumb just across the valley). Really nice woodland setting and some entertaining problems on pockets, some slightly harder stuff available if you don't mind traverses. Most of the stuff on UKC can be highballed at varying levels of scariness. If you venture over to Correges take a big stick, the path along the bottom might be a bit overgrown at this time of year.
Sally in the woods is a similar story with the added bonus of being more scattered, so finding the problems can be a bit tricky for a first visit.
As mentioned Ubley is very limited. Lots of stuff on UKC but it's basically a couple of very minor buttresses where you can climb anywhere at about font 4+/5.
If you've got a rope and shunt handy the routes at Split Rock are pretty good. There's also a very minor wall towards the left hand end where you can make up some eliminates, you'll need to be pretty desperate though! Imagine a wall ~1/3rd the size of minus ten at stoney...
If the grip of mendip lime is strong on your soul you could try dinder wood, some pretty good routes that make scary solos.
There's some really good problems at cheddar but they're quite spread out and pretty limited. Tombstone cave is your best bet for a quick hit, there's tombstone itself at 7C then some good 7A/+ things (bring tape gloves though).
If you can get a bit further afield then bourton combe near bristol has some decent travs.
Ladye Bay near clevedon has some good bits, though the rock quality is a bit suspect in places.
Lots of other bits of esoterica in the bristol area if the above isn't enough to whet your appetite! UKC is fairly comprehensive.
