Camping is tight in yellowstone, first come, first served. If you can camp outside the park, and go on day trips.
THe east gate from Cody is a mess, highway construction, but the best camping is on that highway. The North Fork. Another alternative is go north of Cody to dead Indian, long hual but beafutiful drive, go through Sunlight Basin to Cook City, lots of places to camp there and not near as busy as the North fork. Thats how we go in and out of the park until the constrcution is done. Longer drive but just as beautiful.
As for wildlife, you see thousands of Bison but that is about it. We went three times this summer, I do lots of photography and have done so for 15 years. On all three three trips not a single elk or moose. My only conclusion is the 300 or so wolves in the park have to eat,.
And a Bison is to tough to tackle when you have or had lots of elk calves.