In order to give you a better answer, can you say where you going from and to? What is your preferred riding style, i.e. low traffic roads or the shortest route? Are you self-contained or will you need restaurants for every meal and/or motels along the way?
A short answer is to look at the Kansas State Bicycle Map
http://www.ksdot.org/burRail/bike/biking/KsBicyGuid.asp and the Nebraska State Bicycle Map
http://www.dor.state.ne.us/docs/bicy...-current-2.pdf and do what you feel is appropriate for you.
I have ridden from Mexico to Winnipeg via Tulsa and did eastern KS & NE. The winds can either be a blessing or a curse. Some days I would do a century in 6-7 hours (fully loaded) and then the wind would come as a very strong headwind and I would creep along at 5mph.
People are friendly, most non-large towns have somewhere to camp (may just be a city park). Biggest hassle is the rural area is dying off so finding restaurants and motels can be a pain.