took my two lads, 4 and 6, to Giants as far as the top of garlands. No probs. Boss Aven is proper impressive to a newbie caver.
Agreed, way better that scrotting about is carlswark and hillocks which offer little in the way of inspiration.
Bagshawe is another, though not as 'nice' or as clean as Giants. Walking/stooping all the way to the Main drag by the dungeon. Walls are, on the whole, muddy to the touch so you'll get muddy scuffs on clothes etc. plus a couple of knee deep muddy pools to wade through. (unless you just go down the steps to the chamber at the bottom which is perhaps slightly un-inspiring to say the least and could be done in 5 mins or less)