This really is a tough question. Here are my thoughts. To give you a bit of background, I grew up in SW Montana and lived there until around age 34. I then moved to SW Idaho and have been here about 5 years.
1. My favorite "thing" to hunt is beautiful country. I am drawn to big wild places, often in Wilderness. The specific animals that I am hunting are secondary to the scenery, adventure and challenge. Luckily for me, many parts of Idaho and Montana are tremendously beautiful and are also home to elk, deer, moose, mountain goats, bears, wolves and mountain lions.
2. Bugling elk. I have chased them in the Missouri River Breaks, at 10,000 feet in Central Idaho, sneaking off alfalfa fields in low foothills, etc. The point is, when they are HOT, it is one of the coolest experiences you can have in the outdoors, plain and simple.
3. Antelope archery, spot and stalk.
4. Whitetail archery hunting from a treestand during the rut.