Hot Springs National park in the city of Hot Springs, Arkansas is both the oldest and smallest US National Park. As you can probably guess, the order of the day are steamy hot springs but unlike many other national parks, a lot of Hot Springs National Park's charm lies not in its nature (which of course is excellent) but in its history. The entire north end of the city of Hot Springs, Arkansas is encapsulated by the park and you can visit many of the historic bathhouses like Lamar and Ozark bathhouses, and the especially beautiful Fordyce Bathhouse.
If you'd rather escape a bit into the woods, well, there are plenty of areas for that too. The northern end of the park is full of pine forests and you can see animals like squirrels and raccoons. There's one trail called the Hot Springs Mountain Trail that's especially nice; it takes you up the ridge and back down through the forest and doesn't take more than an hour or so (if that) to complete.