I lived and cycled in Wichita from 88 to 96. I was stationed at McConnell AFB and I pretty much split my time between road/off road. Since I've left Wichita has really grown with houses popping up every where. So since I've been gone the areas I'm describing may have been built up over the years. But I used to spend most of my road riding to the east and north. Out to towns of Rose Hill, Douglas, Lathum, Mulvane,Udall, Rock had some good country riding just to name a few. yes it's mostly flat and windy but when you get to the Flint hills it can be pretty hilly. Roads were in good shape and I never had any problems with the drivers.
Off road there isn't much unless you want to travel. Boeing hills, Sante Fa Lake and Pawnee Prairre are close and have some ok trails but nothing to brag about. Some great dirt roads out in the Flint Hills and Smokey Hills with a few decent climbs. Do a google search for Wichita cycling and it will give you some good web sites to go to.
After Wichita I moved to Spokane Wa Which this place "Rocks" if you a cyclists. Glad I left KS. IMO.