I've been to Yellowstone three times now, and will keep going back as often as i can. In fact we'll be stopping for a couple of days the end of May on our way to the North Cascades.
As you're driving through the park, if you see a lot of cars pulled over that usually means - BEAR, so keep your eyes open. Lamar Valley is a good place to search for wolves as well. Look and listen for any reports of a fresh kill or carcuss, that will be a place to be for bear or wolves as well.
Elk like to hang out by the hotel in Mammoth. Buffalo are every where so don't be surprised if you get stuck in the middle of a "buffalo jam". My wife and I were surrounded by 75 of them one day last year.
I agree with the other members here, Yellowstone for wildlife and the Tetons for landscapes. Though there are some good places to get lanscape pictures in Yellowstone as well. Be sure to get a park map, and talk to the rangers. My stepson is a ranger there and we always talk to them to find out where the wildlife are hanging out at.
Have fun and enjoy the trip