I was reading this thread again and thought I would add my opinion.
(TJ this in case if you haven't gone solo caving yet).
ALWAYS WEAR A HELMET no matter how easy/large is the cave and ALWAYS CARRY AT LEAST 2 RELIABLE WATERPROOF LAMPS WITH NEW BATTERIES.
I would try Shakespear's cave and Ogof Clogwyn in Clydach Gorge, South Wales. If you are driving you can park nearby and there's also a bus stop nearby.
However Shakespear's Cave has a few ducks which mean you will have water up to your neck (if you have no wet suit you gotta be really brave to venture the extremely cold water) and have to duck your head to go through. I would go in the summer when it's drier and make sure the forecast says there's no chance of even as much as drizzle.
But for Ogof Clogwyn you only need wellingtons as the water will at the most go up to your knees.
When you get to the entrance you need to free climb up to the upper shelve and that's the way in. Great fun and beautiful phreatic shelves (if you like watery places). And you can not get lost here.
For drier option Aggie as mentioned here before is good too and slightly bigger/longer than these 2.
But just make sure you do tell someone that you are going there and call them back when you are safely out. Caves are fun but really dangerous if something goes wrong and there's no one who knows you there.
