According to this story [Link], a 13 year old girl found a nearly 3 carat diamond at Crater of Diamonds State Park [Link], a state park in southwest Arkansas.
I've been there. Didn't find any diamonds, but I had a great time trying! I tent-camped, followed the hiking trails to the river every morning, and prospected every afternoon. I definitely plan to return. It's like lots of my favorite places, not on the way to anywhere. Ya gotta be specifically going there.
Not only that, but Arkansas is one of the most camping-friendly states I've visited. Lots of state parks, state parks all have a campground (unlike some states I've been to; neighboring Missouri for example) and campers are welcomed even if they're driving a cheap old vehicle or RV. No matter what you're driving or where you are in Arkansas, you are probably within 20 miles of a cheap, decent place to camp.
Oh, and people really do find diamonds in Crater of Diamonds SP, and there is an assay office in the nearby town.
I recommend it as a fun place to go.