Take a 40 minute venture out to Matlock, there's a decent sized cave with an entrance near one of the hotels. Took us around 2 hours to explore, seems to be some older graffiti inside ("X was here, 1989") etc. Pretty cool, little bit of a squeeze to get in, and a couple of bits to climb but all in is a pretty easy explore too. Still has remnants of the old cart tracks that ran through it.
There was an old mine or quarry that people used to go and explore which was apparently miles better. First time I went off though, I managed to trigger one of those tripod alarms and was found stood next to our car pretty quickly by security who were pretty cool about it, just told us to leave and that was that.