I think there is a pay to use area near Omaha, but the closest OHV area is around Tuttle Creek near Manhattan, KS. Some pretty decent wheeling for Kansas and your best bet. People there every weekend.
You might contact the Flatlanders Jeep Club, they've always had an anual event around May that is open to all makes and a lot of fun.
I used to live in Lincoln, it's 2 hours from there.