The Wind River Reservation near Lander does not have much to see. IMHO. There is an old cemetary north of Lander that has the graves of Sacajawea and Chief Washakie.
The west side of the Wind River Mts. are much more interesting to me. There is the western town of Pinedale and many mountain lakes and streams. And there is the site and museum of the first 1825 Mountain Man Rendezvous in the west. About 20 south of Pinedale on the road to Rock Springs, the old Oregon Trail crosses the highway.
But if I had to choose between going back east this direction or through Cody, I would not miss the museum in Cody.
"The Snake is rarely dangerous in that stretch because the water flow is primarily managed for tourism (commercial rafting) and not irrigation."
The water in the river is controled for the irrigators of the State of Idaho, who own the water rights to it. Commercial rafters have to use whatever water comes down the river.
The irrigation need STARTS with Palisades Reservior, the water for irrigation is stored there and below Palisades dam is where you see fluctuation of water on the Snake. Above Palisades there is minimal use of or need for irrigation water so the flow from Jackson Lake is fairly constant and does conveniently serve the needs of commercial recreation in the form of rafting in most normal water years from Jackson to Alpine. The Snake river from it's start to where it enters the Columbia can hardly be called a "wild river" at any point--too many dams, too many spillways, too much use of the water for irrigation and power generation. I doubt that there is a river in America that is as controlled in terms of flow as much as the Snake. However, if you think that the commercial rafting out of Jackson is "dangerous" then the OP should pay attention and might want to check up on the number of deaths and injuries that result from those commercial rafting trips annually. I'm sure he will find most customers are hurt getting into and out of the buses and boats more often than when on the river rafting.
Horrors!! Billy's Burgers and the Cadillac are GONE. I hear the lease ran out and the landlord doubled the rent. So they split. Too bad. Great burger. It is happening to other businesses as well. 20 yr. leases are up and the landlords are jacking the price up. Some of these businesses can't handle the extra overhead.
White water rafting with an outfitter is not generally dangerous after the spring run off. Have done it and it is safe enough. Just don't try to do it on your own. Go with a pro.
Actually if you only have one day you may as well just drive through Grand Teton NP. That's about all you will have time to do. This is my 8th summer here and I'm still seeing and doing new stuff. Most people just drive through. But if you love the outdoors, you can spend a liftetime here.
IMHO there isn't much to do in the town itself but eat and shop. The real action is the nature around the town. Of course we do get an occasional bear or moose in town.
Stop in the visitor center on the north end of town for lots of info. Those folks know what's going on.