If you're going in late Spring, after all the roads are open, or Summer, you'll probably want to see the usual tourist sites like Old Faithful, Mammoth Springs, the Geyser basin. For wildlife Lamar Valley (good area for wolves) and Hayden Valley. Or just drive the main roads and look for cars stopped on the road. I've heard Mountain Goats frequent the area around Mt. Washburn. Black bears: any road, anywhere. Grizzly: I've seen them in Hayden Valley and one on the road to Mt. Washburn. I've heard they can also be seen in Lamar and around Blacktail Pond (it's on Google Maps).The general area.
Our guide said that another good spot is the Blacktail Ponds. Bison tend to wander into some of the pools, get stuck and die. The Grizzlies come along and pull the Bison out.Good time to see griz is first couple of weeks in June when the elk calves drop. Set up with a scope during that time in Lamar or Hayden Valley and you'll be sure to find them making grid patterns through the sagebrush. Elk calves are born with minimal scent so the grid pattern works best for finding them. Once they do find an elk calf, they lay down on it and start eating while the mother stands by and watches helplessly. It's incredibly brutal but awesome to watch play out.