There are a great many "shafts" around Rhosesmor (beehives) with a tremendous amount of lead workings underneath. Sadly (but inevitably) most are now inaccessible.
There are some though, that can still be accessed.
Also, of course, underneath the lead workings is the Milwr Tunnel (as per Roy and the links he provided above). There is no access to the Milwr tunnel in Rhosesmor ... you have to wander a little afield to find any of the very few entrance ways.
The link Roy gave you (above) is excellent for information and you can also try the knowledge bank (and forum) of the local caving club which meets a couple of miles away ...www.ucet.org.uk