To put it plain and simple IL draw for licenses is just plain screwed up! The whole state typically sells out in a day, but I've heard tail that they may be changing things this year since the Outfitters of the state have been raising a big stink about losing buisness b/c of their draw system. Putting a cap on the licenses hurt the Outfitters in any state....
As of last year you applied around (I believe) 1st week in June? (but I may be wrong) and the tag + license for a non-resident ran you around $270-280.
I believe that's in Marion County? Now I've hunted just SE of that county in White and Wabash. That whole area has some huge bucks in it, I'm sure but I haven't personally been around Salem to vouch for it.
Here's the IL DNR website for more info
http://dnr.state.il.us/admin/systems/
and last years season / dates
http://dnr.state.il.us/admin/systems/huntdates.pdf