Outlaw Cave, where Butch Cassidy and the Sundance Kid hung out. This is of course in the middle of some BLM land so you will have to work around hunters.
The Invasion Bar in Kaycee has some good hearty food, gotta try the mountain oysters (or whatever they call them there). The other place to eat is the hotel, it has good food to but I cannot remember the name.
Head north to Buffalo and you have the outdoor store, the Sports Lure. It has all kinds of maps, lots of cool gear you dont need but think you do and some nice taxidermy work. Buffalo has a McDonalds, so once you get your craving for modernized food you can get your fix there. Once in Buffalo you can drive up into the Big Horns and check out the high country or drive over the mountain and head to Yellowstone or drive to Thermopolis Hot Springs to soak in the mineral baths! Buffalo also has a few liquor stores so you can grab some good local brews of the Mountain West.
You can drive further North and go to Sheridan. The regions Game and Fish office is located there.