Dan,
I have hit quite a few spots in the NC mountains with my family. My son is really into the gems and has quite a collection now. We've been to the Gem Mountain in Spruce Pines that was on the Treasures TV show the other night. It's a great place to take the kids for some fun, but like Ram mentioned, these buckets are salted, so who knows if they have any good finds in there? You may want to watch out for some of these places that try to lure you into having some of your "fantastic" gems cut and made into jewelry. I spoke to a local gemologist in that area, and he informed me that they basically just switch out your "fantastic" gem finds with ones they already have cut. Just thought I'd throw that out there.
Another place we like on this link:
http://www.broadrivergemsandmining.com/index2.htm
It's not as crowded, and is run by some very nice folks. It's worth going just to see the gift shop / museum that the owner Russ Wood has there. Amazing stuff. He's very informative too. I usually bring my gold panning stuff and go down to the river to prospect while the family is doing the gem hunting.
There is a great gem/mineral/fossil museum set up in the old downtown area of Hendersonville too. Very neat stuff, and the kids can pick out and crack open their own geodes too. Here's that like:
http://www.mineralmuseum.org/
As far as gold, I've been to Thermal City panning before. A lot of fun, but I never found anything yet. I'm sure others have though. I've only spent about 4-5 hours there thought. There is another place (smaller operation) about 1/2 mile down the road from Thermal City too. They salt the buckets too, but it's a lot of fun finding even gold flakes in you pan. It's worth going just to learn some of the panning techniques.
I've tried panning in some of the local rivers in that area, but have only found one small flake so far by myself. Even though it was small, it was exciting to find that piece, and just knowing I found it on my own.
I usually bring a 5 gallon bucket with me, wade out into the rivers, and fill the bucket with soil. Then I can bring it home, and pan through it at my leisure, instead of trying to do it with my wife and kids screaming.... "can we go now?"
Anyways, you owe it to yourself and your family to check some of the places out. It is a great time for all.
Just don't think you are going to find all those great finds at everyplace you go to, like the lady that hosts that treasure show. If I found gold, diamonds, opals, gems, etc. everytime like she does, I could retire early.

It sure makes the viewing exiting though, doesn't it?
Good luck and have fun with the family,
MM
P.S. Here's another event you may want to check out this spring:
http://www.ncgold.org/