It's a small town that can be covered on foot, but if you want to travel in style, use horse and buggy. Wyoming Carriage and Taxi, +1 866 646-2723,  runs sightseeing horse-drawn carriage rides in town during the summer months.
Soak in the waters from the hot springs. There are several commercial operations that use the waters with varying degrees of gimmickry, but in addition, the town maintains a bathhouse that is free (under the terms of the treaty whereby a local Indian tribe ceded access to the spring in the 19th century) and open to the public during daylight hours.
Las Fuentes, 530 Arapahoe St., +1 307 864-3192. Mon-Sat 11-2, 5 to "closing." Surprisingly good Mexican food, with a "New Mexican" slant; the "Maria," the house-special burrito, wouldn't be out of place in Santa Fe.
Best Western Plaza Hotel, 116 E. Park St., +1 307 864-2939. An historic hotel on the grounds of the state park, recently renovated and merged into the Best Western chain. A small spa/hot tub (no aeration) draws waters from the spring. Not a large place, so if you're interested in it, be sure to reserve, or at least inquire, in advance.