If you're asking about Yellowstone/Teton, the one "must do" hike is the Canyon Cascades hike out of the Tetons. It originates out of Jenny Lake. I would suggest taking the ferry across Jenny Lake to the trailhead (you can hike along the shoreline if you prefer but it adds a couple of miles each way). You will hike up past Hidden Falls and Inspiration Point. This part of the hike is quite crowded. But then if you continue on past Inspiration Point you enter Cascade Canyon. The trail levels out from there and you lose most of the crowds. And the views along the Canyon are spectacular. Go at least a couple of miles in the canyon before returning. Awesome hike.
If you're referring to Glacier, the link in this thread has several good suggestions. Glacier is a hiker's paradise. Jaw dropping scenery everywhere. It's the closest thing to the Swiss Alps you'll find in the US.