Have close encounters of the animal kind.
So many critters (marmots, squee!) call this wilderness home that you will likely cross paths with a few, but if you want to leave it less to chance, book a Jackson Hole Wildlife Safari. The guides, most of whom dabble in photography and can give helpful hints, pick you up at the hotel with breakfast and then drive around looking for moose, deer, birds, bears, and bison in their typical hangouts while talking area history, park trivia, and flora and fauna facts. They're also in constant communication with each other to share sightings. There are half- and full-day options offered in both national parks. If you are really lucky, you'll catch sight of a wolf pack. (Increased chances in cold months.) Also in cooler months, you can spot elk congregating at the national refuge between town and the park for free.