Ok, I'll admit it, neither
Mud Volcano nor
Mammoth Hot Springs are the prettiest places in Yellowstone. But they are interesting because they are different then the typical landscapes you would see elsewhere.
Mud Volcano is where the not pretty is emphasized. Unless of course you like mud... The landscape here is similar to several other areas of Yellowstone, except instead of pretty water there is a mud like substance. Mud Volcano was discovered in the 1870s, and "went off" shortly after. It has left behind as a smelly, bubbling spring. It would be wrong of me not to warn you, the place smells of sulfur or rotten eggs. But because of its uniqueness it's worth a quick visit, I just would choose to do a hike in this area.
Mammoth Hot Springs have an interesting formation, from the NPS website,
"The step-like terraces form as heated water moves along the Morris-Mammoth Fault. The hot water carries dissolved calcium and bicarbonate to the surface of the terraces where pressure lessens. Carbon dioxide then escapes as gas and the carbonate combines with calcium to precipitate as travertine." This means that the formations are constantly changing. You wont notice a difference from day to day, but if you visit years later you may. If you climb to the top you'll get the payoff - the view of the valley below is gorgeous. So, although it's a hike to the top, it's worth it.
