This is a 5 year old thread, so I hope the OP had a good visit to Yellowstone.

I live about 100 miles north of Yellowstone, and I usually make a couple of visits to the Park every year. My last visit was earlier this month, and the Park had just opened their newly remodeled visitor center in Mammoth. The center was well done with many new displays, except for the mountain lion. That is one of the absolute worst taxidermy jobs that I have ever seen, and they labeled it with the Latin name of "puma concolor".

As others had posted, the river bottoms like the Lamar, Yellowstone, Firehole, and Madison are some of the best places to view the larger animals. Buffalo can be seen along most of them as can an occasional elk. Bighorn sheep used to be commonly seen on the hills above the Gardiner River between the town of Gardiner and Mammoth. There also used to be a herd of bighorns that wintered close to the junction of Pebble Creek and the Lamar River. There are usually a few elk in the Mammoth area, often in the yards of the buildings and houses.

Since the Park introduced the Canadian wolves in the mid 90s, the numbers of large animals, like elk, has fallen drastically. For example, the official count of elk in the Northern Yellowstone heard has gone from 22,000 plus animals before the introduction to less than 4,000 animals this year.

Its now very rare to see a bighorn in the Gardiner/Mammoth area, and the last time that I looked for sheep in the Lamar area, the Park had posted the sheep wintering area as closed to human entry to protect wolf denning.

It used to almost always see one or more moose in the willow flats in the upper Gallatin River/Cougar Creek area of the Northwestern corner of Yellowstone. Its been over 10 years since I've seen a moose there.

A number of years ago, the Park installed a high-tech laser system for several miles along the road next to the upper Gallatin River. This system would detect elk crossing the road, and flash warnings to motorists. They have since taken the system down as there are no longer the great herds of elk that used to cross there.

On a positive note, our last few trips to Yellowstone, we've seen three grizzly bears (or maybe the same bear on subsequent trips as two of the sightings were within a few miles of each other) and a black bear. All of these bears were within 1-200 yards of the road, and caused huge traffic jams.

A spotting scope and telephoto camera lenses are always helpful for good viewing and photographing wildlife.