In reply to Co1in H:
Dinorwic slate quarries are where you want to be. This is where the famous routes are, 'the quarry man' etc. it's very atmospheric, and still has lots of evidence of its quarrying history.
If you're up for a little abseiling you can google a tour of the slate quarry called 'snakes and ladders'. It's a scramble/walk/abseil which will take a couple of hours to complete. There is one HVS section which involves climbing up an old chain (but this can be bypassed).
Otherwise just go for a wander. If you park at the mining museum there is a nice walk (although quite steep) to the quarry. Otherwise you can park at Bus Stop quarry and take a nice flat walk into the quarries.
If you're looking for somewhere to stay there are plenty of options in and around llanberis. Camping b&bs etc.