The Mammoth Hot Springs Hotel is worth a visit even if you're not staying. Piano music echoes around the lobby from 5pm, followed by video or slide presentations in the Map Room at 8:30pm, where you can also check out the huge wall map of the United States assembled using 15 types of wood from around the world. There's also a charming antique water fountain to the right of the gift shop.
Robert Reamer (of Old Faithful Inn fame) designed the hotel in 1937, though the previous National Hotel stood nearby from 1883.