Here's the deal:
If you've never been there, it is massive. HUGE. The park is laid out in generally a figure 8 shape of roadways and each node is roughly 2 hours separated (once you factor in traffic jams etc).
There's literally something to photograph at every stretch of the road. Bison will be present virtually everywhere in the park, but Hayden and Lamar areas are focus points for 4-legged animals in herds. Elk will be more present in the forest areas, bison, antelope etc in the wider-open areas, but those are strong "Generalites".
Waterfalls are interesting but expect crowds of tour buses full of people hoping to get a quick selfie a the "Best spots". You will see what I mean as soon as you try to get to see any of the "major" destinations.
Geysers and hotsprings are focused mostly on the west side, at Norris and the lower gyeser basin, but there's some cool views and landscape shots with the lake down at the west thumb geyser area.
Grand prismatic spring is beautiful, especially with early morning or evening sunlight, but the bright colors will show best with direct overhead sun.
For bears - your best bet is to watch for huge traffic jams and ask around at the gas stations and convenience stores, they are usually listening to traffic radios and will possibly have insights. You're really lucky if you spot one and nobody else is there, but that's probably not going to happen.
Mammoth Hot springs are pretty cool, not a LOT of active photography there, other than some historic buildings and the springs themselves. There will be a few animals around there too, we saw herds of elk just laying in town.
There's two good photography guide books that I found helpful... I will try to find the titles and share them back here.
Edit:
Guide book 1, Guide Book 2
For some of the best animal viewing - evening - just before dusk seemed to be best when we were there. Just be mindful if you wander far from your car, that predators are around and might be taking interest in you. Wolves and Bears are the main risk. Carry Bear spray and hope not to use it!
My biggest piece of advice. Focus on one area or segment of the figure 8 roads per day and spend your time there. You'll spend your whole day in the car otherwise. Pack some food/drinks and snacks so you can multi-task... drive and eat at the same time.
Another piece of advice - be a little "sneaky". If you show up with a tripod and a 600mm White lens you're going to draw the looky-loos. Sometimes that's good, you can offer to let someone look through your lens to see something WAY In the distance and make their day. Other times, you can quickly draw a crowd and ruin your good opportunity for a photo. I shot my whole trip with 2 lenses. A 100-400 and a 16-35.
One area outside of the park that is not often discussed is the northeast entrance and the Beartooth highway. Some GORGEOUS views up there and WAY less crowding.