If your in the peak district, the best place to aim for is Castleton. Here you'll find the classics of Peak/speedwell (although 3rd partly liability insurance is needed) Giants and P8(jackpot) super stream ways - Eldon Hole (big vertical open pot). Nettle pot. Oxlow. Bagshawe.
There are also 4 excellent Show Caves with guided tours. Peak cavern (the largest cave entrance roof in UK) where the village of castleton began. Speedwell - an underground boat trip along an old lead mine canal, Treak Cliff Cavern - See the veins of a semi precious gem stone (blue john) that is only found on this hillside plus stunning decoration in the lower caverns and finally Blue John caverns, The same as treak cliff but with more blue john and less pretties.
I usually cave in the week day evenings if you want an for an evening trip. contact me via this site - use PM (private message) feature if you like.
South wales is where all the caving is - unless you fancy huge old slate mines, but they are a bit wild. Having said that - if your in LLanberis at the foot of snowdon mountain - the old Slate Quarries are well worth a wander round on a rainy day.
Hope you enjoy yourselves -