Not to be a debbie downer but KS has the smallest amount of public land of any state the US and it gets pounded. Your best bet for anything is going to be SE KS but getting a 140 off of public is going to take a LOTTTT of work. Your not going to go in on a weekend and just pick one up. Most public places are good for a doe over a weekend if you get luck but you need to be in there early in the season or hit the needle in a hay stack. As an examaple up at Jamestown a guide was charging out of state hunters $1500 a person to walk them out to his stand on public land. He had 9 stands in one tree row and was just walking guys past each other from stand to stand... With the law changes this year where you can't leave a stand out on public land he lost a lot of money.
Despite what KDWP tell you I have been hunting deer in KS for 15 years and never shot a 130+ deer, granted I spend most of my time duck hunting and crappie fishing and only rifle hunt a few days a year. Good luck to you if you come but plan on at least a week to scout and break down an area.