I believe the closest is eastern Kentucky. Colorado next closest. I have no experience in elk hunting. But, I am under the impression that it is not simple for a midwesterner to self guide themselves to an elk. I have two friends who bagged one with archery equipment on their second year of trying. They were self guided, young, and determined.
If you can afford an outfitter, your options increase exponentially.
Archery elk is on my bucket list. Just haven't seriously moved towards making it happen.