Just went to Yellowstone today. Spent time at Mammoth Hot Springs and in Lamar valley. Saw a grizzley just South of Mammoth and a black bear in Lamar plus lots of Bison. Got to the West gate at around 6:30 AM and had 2 cars in front of me. In Lamar (around Noon) I had lines of cars coming in from the Northeast gate. Around 1 PM the park really filled up. On my way back from Lamar (there's only one way you can go as Dunraven pass between Tower and Canyon is closed) around 2 PM the lines in Mammoth were about 30 people long to get into the general store and for places for food. Oh, and there was an Elk in the middle of all the people calmly eating grass. Only took around 300+ images. The terraces at Mammoth really photograph great early in the AM as the shadows make them stand out. Mid day they wash out and you really can't see the terrace effect. A few more places to add to your list are Udine Falls between Mammoth and Tower and the Firehole canyon drive. The waterfalls were spectacular at these locations!
There are no hikes you should go on by yourself, however if you wait at popular trailheads such as Fairy Falls, Mystic Falls, Trout Lake, etc., you may find a group that you can join. Be sure to carry and know how to use bear spray. Bears can be anywhere even on the boardwalks. That being said, you may not even see one while you're in Yellowstone. Timing is everything with wildlife photography. The wolves are often seen in Lamar Valley right before or after sunrise, but I've also seen them there later in the day. The same goes for Hayden Valley. The wolves and bears like to be out early and late unless there's a carcass around. That's your best opportunity to find them. Bears will go out in any weather if they're hungry, so don't depend on them hiding if it's raining. As far as night photography goes, I'd stay close to your car. Since you're staying in the Gardiner area Mammoth Hot Springs might be a good place to start. You could park in the parking lot close to Liberty Cap and possibly get night pictures with some of the terraces in your shot. I hope this helps.
Consider contacting some professional photographers in the area. John Gerlach
https://www.gerlachnaturephoto.com/ is one that I know of. John live just outside of Yellowstone and knows both parks well. Connecting up with a photographer will likely cost you some money but the knowledge in the area, where to get great photos, camera learning and having a guide will be worth every penny.
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