Riverton has Wyoming's only casino. Which is cool. There's also some excellent hiking, fishing and camping in that area.
But the Wind River Reservation is right there, which can cause problems. I've visited Riverton many times, and have had friends who lived there. What I'm about to say is not racially motivated, these are facts from personal experience and stories told to me by people I trust.
Anything you put outside that isn't bolted down, and some things that are bolted down, will be stolen. My friends that lived there had the propane tank off their barbeque stolen several times. They had the spare tires stolen from under their truck. Those cheap solar powered lights were stolen from their front yard. Their kids bikes were stolen in the middle of the day when they were left in an open garage. Lock your stuff up tight.
Make sure your car insurance covers you against uninsured motorists. Mine didn't the first time I was there, and a resident of the reservation decided to drink a case of beer and go for a drive. He crossed the center line and hit me head on. He had no insurance, and I have no recourse since he lives in a sovereign nation and is living off the government payouts. I've heard this same story from dozens of people from that area.
It is not a bad place, you've just got to protect yourself and remember that the rules don't necessarily apply to everyone like they should.
eta: The box men at the craps table don't seem to understand the odds and calculate payouts correctly. Gotta watch them.