"Hunt where the elk are" is what my friend Tony taught me when I started hunting 30 years ago. Good to hear it again. Like a lot of new hunters, I figured I would find some sign, then sit in a place and hope they came by. I learned from him that won't work, you'll sit there all day. Instead we scouted hard for the 2-3 days before a hunt, and found a herd or a harem then followed them until the opening day. It involved a lot of hiking and sometimes riding mules, or 4 wheeling into very remote places. Then glassing a lot to find some. After you do....the shooting is the easy part. We often camped right next to a herd, in the timber, the night before the opening day. You wake up at oh-dark-thirty, tiptoe out to the edge of the treeline, wait til the light comes up, fire. He was raised in Wyoming by wolves I used to joke. We met in NM at work, then were best friends in NM an AZ for 25 years. He died a few weeks ago, 65, of cancer. Miss him a lot, and will for life.
What is amazing is compared to deer you can get very close to Elk, like tecum0tha says. I've been able to walk or ride within 25 yards of elk many times over the past 30 years, in mountain timber. Like jackrabbits, they like to hold until you are almost on them. They make a lot of noise, so you can find them in the woods, or little clearings. And you won't scare them just stepping close, breaking a few sticks, etc. Any gun you make that will hit out to 100 yards should be accurate enough.
The key is to find them and then be in shape to get close before some other hunter fires a shot and they slip into the timber. I've seen a small herd several times out grazing in the pre-dawn fields, slowly heading towards timber as they graze as the light comes up. About sunrise they're within 20 yards of the treeline, still grazing, then if they hear a vehicle coming they just step the few feet into the trees. I watched them doing this several times, scouting on foot. They almost always are out of sight the last 30 seconds before the truck rounds the bend into sight. The truck drives slowly by, hunters expectantly looking out the windows on both sides. Not knowing that 50 yards away I'm sitting, and also a herd is in the trees on the other side of the clearing. For every herd you DO see, there are 20 you never saw.