The park is large and ideally you will want to spend at least a few days. The Old Faithful Lodge is one of the most famous lodges to stay in the national park system and is conveniently located right in the heart of the park.
The Geyser fields around the lodge are one of the main attractions of the park but can be hard to photograph.
Mammoth Hot Springs has some nice calcified rock formations worth photographing. It's one of the most unusual places in the park.
The Grand Prismatic Spring is a colorful pool that can be viewed by walking on the boardwalk that leads up to it. A better view can be had by climbing the hill behind it to get a bird's eye view. It's my favorite thing to photograph in the park.
Upper Yellowstone Falls and the Grand Canyon of the Yellowstone is a can't miss place to visit. It's hard not to get a good picture from the overlook at Artist Point.