Hot springs, bison, and gorgeous views of the Bighorn River.
The deep anticline underlying Thermopolis, Wyoming has resulted in an abundance of hot springs, some of which flow directly into the Bighorn River and creating a wide variety of multi-colored pools and bubbling creeks. Most of the features are contained within the aptly named, Hot Springs State Park, which in addition to having for-pay soaking pools contain several excellent hiking trails.
One such trail is the Spirit Trail, a 1.3 mile trail that loops around the northern end of the park and includes some excellent overlooks of the Bighorn River, a Bison herd, Black Sulphur Spring, and the Devil's Punch Bowl.
Getting to Thermopolis, Wyoming is the biggest challenge, as it is about 3.5 hours east of Jackson, 4.5 hours from Laramie, and 3 hours from Sheridan. That said, it is a worthy side trip particularly if you are planning on going to Yellowstone or the Grand Tetons and are coming from the East.
Note: the average temperate of the hot springs are 130 degrees Fahrenheit, well above the point to scald and kill. If you are looking to soak, go into the official, designated soaking pools.