Enjoy your visit. You have to hit the popular spots. No way around it. They are popular for a reason. The Lamar Valley will have bison and a lot of other critters too. When photographing the critters you have to take what the park offers. If you have someone with you it helps a lot as some of the roads, while not dangerous, do require your attention. While they are wide enough, shoulders are optional in places. Not that you are going to drive off a cliff, but you may get stuck. A spotting scope and or binoculars are good accessories too. While the animals may be too far off to photograph they are still fun to watch.
Dress in layers. It is a changeable time of year out there. Last May I encountered snow, rain and sleet and hail all at the same time. The bison and elk will be in rut so keep your head on a swivel if you are near them . Watching two huge male bison fight over mating rights is darned impressive if you are close to them. Scenery is all over the place. Especially for east coasters like us. For classic shots of the upper and lower falls. Those are visible from South Rim Drive. Everyone wants the shot simply because they are well worth getting. I am not sure if the trails to both of the falls overlooks are open. There has been some trail reconstruction going on the past few years in the Canyon Village area.
Mammoth Hot Springs well worth several shots from all different angles. I always stay at Gardiner when I go. The north part of the park is less crowded. I try to hit the hot spots early to beat the crowds and then migrate to other areas as the morning wears on. Bring plenty of water with you. Food food. You will be doing a lot of walking in the geyser basins. There is an overlook where you can get an overview of Grand Prismatic Spring. It requires a bit of a walk, but well worth a shot that most visitors are not going to get.
Bring bear spray. They do visit the hot spots too. Humans are not the apex predator out there. More like walking protein bars. They are bulking up before hibernation. Do not be surprised to see a visitor or two carrying a pistol. Usually a large caliber one. They are allowed. If you go into the back country and get eaten by a bear, it is considered all part of your wilderness experience. Personal safely is up to you. Mother Nature just doesn't give a darn about it. Follow the rules and stay on the trails. The warnings in the thermal areas are not suggestions. Cell phone coverage is available in the main areas and very spotty everywhere else.
The park website has a lot of information about conditions, road and trail closures. Also some web cams so you can get a real time weather observation. There literally scenic photographs just about anywhere you can pull off the road. The park scenery changes every day. Pull off and enjoy it. It is more than okay to put the cameras down and just enjoy the park for what it is.
Get the shots of Old Faithful, the two main waterfalls, and Grand Prismatic Spring. Then pad your portfolio with everything else.
I have a K1, K1-II and a K3 that I take with me. My most used lenses the last few times were my D FA 28-105 and D FA 150-450 for the K1's and my Sigma 17-70 a DA 55-300 WR for my K3. Since I drive I have room for all of them. Less used were my 20mm and macro lenses. Tripods are helpful for cameras and scopes. I do not know how you are getting there so I am not sure what kit you will be taking along.
So, in summary, Scenery is everywhere. Hit the hot spots early if you can. Critters are hit or miss so having someone ride shotgun is a big help. Dress for anything, Enjoy the park. As I have gotten older, I find the tourists more amusing than an annoyance. I have started including them in shots at some places.
If you are not old enough to get the senior pass, get the Golden Eagle pass. That is good for one year and once you have it, all subsequent admissions are free. I think it is $35 per car per day to get in. It covers any national park too. I have the senior pass, but I still drop money in the donation jars every time I go.
Cody is a nice place. The Buffalo Bill Museum is awesome and it contains the Winchester family firearms collection. One of it's artifacts is one of the air rifles that Lewis And Clark carried with them. There is also a quirky little museum in Cody attached to a gun shop called the Dug Up Gun Museum. It consist of abandoned firearms dug up at various places around the world.
There is a book available at the park stores, or online called The Roadside Geology of Yellowstone Country. Well worth a read if you are interested in that stuff.
I hope this helps. Enjoy your trip.