I thought the Norris Geyser Basin in YNP was really cool, very unworldly looking terrain. That is not too far south of Gardiner. The Mammoth Hot Springs area is even closer to where you will be. I did not get into that as much as the Norris area, but part of that is I was tired by that point. A little farther south of Norris is the Artists Paintpots trail, which I thought was cool, a bit low-key, but the 'paintpots' are cool. Farther south than this is Great Prismatic Spring, which is also very cool, and very crowded. The best views are supposedly from above, but all the places with higher-up views were closed when I was there, so I just had the standard views from down low.
To appreciate the thermal features in Yellowstone, you really need to see them in person, and see/hear/smell all the gurgling and splashing, which makes them feel alive. Photos do not capture that. And for checking out thermal pools, make sure you have polarized sunglasses, so you can see down into the depths better.