The Greenhow Hill area is about 30 mins from Ripon and is a vast moonscape of old lead mines. The surface remains are some of the most extensive you’ll see. There are odd bits of underground, nothing large though, that we have come across anyhow. Depending upon when you are there we’d be happy to take you to one of the mines that's worth a look.
Pateley Bridge has the very impressive Scot Gate Ash quarries which had underground workings -as did other quarries in the area - but we’ve not found anything explorable yet.
Or, as RJV says, up to the Dales in about an hour. Lots of good stuff in Arkengarthdale, send a pm if you need any pointers.