We have "mined" for gemstones several places in the country, and NC is one of the best. The western part of the state has a lot of old mines, and places you can go to tour or mine.
Franklin NC, in the Cowee valley, is a great place to start. There are a variety of "mines", ranging from the very tourist oriented (great if you have kids) to the more "natural" settings, where the ore is not salted. The latter places usually use tailings from the original mines, and you can purchase buckets of this material to search through in the onsite troughs, using the flowing water to separate out the interesting rocks.
There are also a lot of places to see relating to the mines, including a nice museum, and many lapidary places that you can pay to polish anything you may find, or even set the material into jewelry. If you enjoy rock hunting, the Franklin area is a really fun place to visit!
I must say that it's just for fun. The odds of finding anything truly valuable is rather remote, regardless of what the treasure-hunting shows tell you on TV. This is not to disparage the concept, it's still very fun. We have gone back several times.
One other place I would mention is in Arkansas, interesting because it's the only real diamond mine in the US, a very rare geological oddity in Murfreesboro. This is where the Crater of Diamonds state park is located. It used to be a real diamond mine, producing some nice gemstones. It was purchased by Arkansas and turned into a state park, where you can go and look for diamonds yourself. Anything you find is yours to keep, and every year quite a few nice diamonds are found. This is another fun place to visit.