One of the few places where you can take a legal soak in Yellowstone is Boiling River, halfway between Gardiner and Mammoth. From the parking area by the Montana–Wyoming border a trail leads 0.5 miles along the river to a point where an underground hot spring surfaces from below a limestone overhang, mixing with river water to create the perfect temperature in several popular artificial pools.
Bring a towel and flip-flops/river shoes. The only changing area is the vault toilet at the parking lot. There's a picnic area across the road. Swimming is allowed only during daylight hours, and food, pets, alcohol and nudity are prohibited. The pools are closed when river levels are high (most commonly in spring and early summer until July). Be aware of the potential dangers of soaking in hot springs.
The turnouts north of here are good places to spot pronghorn in the summer and bighorn sheep and elk in the winter. Also to the north is a sign that marks the 45th parallel, halfway between the equator and the North Pole.