Ditto on the Grizzly & Wolf Discovery Center in West Yellowstone. It's worth a morning or afternoon, especially if you are not having much luck seeing the wildlife. Moose are probably best seen outside the park, in the Island Park area of Idaho (back on the gravel roads off the main drags) - they have become relatively rare in Yellowstone over the past few decades, due in part to change in habitat in the park after the fires of '88.
Black bears may be hanging around the Tower Fall area (not in the parking lot), grizzlies more likely in Hayden Valley, in the Pelican Creek area near Fishing Bridge (do NOT hike there w/o letting rangers know), and over Dunraven Pass. That said, there is far from a guarantee - as you know, Yellowstone is not a zoo and the individual animals are not "managed" closely unless they happen to prove a problem getting too close to people.
Best way to see wildlife: wherever you see cars pulled off along the side of the road, there is usually something to see. It may be an elk or (more likely) buffalo (bison) but it could be deer, bear, moose, etc. (We did see a moose in Yellowstone 3 years ago.) The animals move around a lot to find food (or peace & quiet away from all the tourists
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Some less-well-known park residents that are fun to see: bighorn sheep and pronghorn antelope. More likely near the north entrance and in Lamar Valley (northeast section of the park). Lots of elk hang out at Mammoth, though we have been there & not seen any some days.
I've been going to Yellowstone fairly frequently for the last 50 years and have yet to see a wolf.
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