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I'm 30 and have had the opportunity to take 160-180 class Whitetail every year as my parents live in Illinois. I have always wanted to go Elk Hunting and I figure if I don't attempt to go or try plan something I may never do it.
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I grew up in IL. Ironically I miss whitetail hunting sometimes, sitting in a stand and how easy it is to get tags, long archery season, ect. Like others have said, once you get an elk it will ruin you, you'll be addicted. It's a lot different and it's a lot of work especially on a public land DIY hunt.
For a "trophy" bull you're looking at 6-10k just for the hunt alone and most likely it will be a private land hunt. There are plenty of options out there between Idaho, CO, Utah and New Mexico. If you decide on public land, get an outfitter and/or semi-guided drop camp somewhere.
If you're not worried about a trophy there are plenty of hunts in the 2-5k range that will allow you to harvest a decent bull with a guide.
If you want to go DIY public land I would say either muzzle loader or archery is the way to go. The elk are less pressured, it's the rut and you'll get more action as far as calling them in. Regular OTC rifle seasons are usually crowded (at least in CO) and it sounds like you don't have any preference points built up for the trophy or better units?