I like to check the Strava Heat Map when I'm going to unknown places. It's a year of uploaded GPS recorded rides, color coded by popularity--bright red is the most commonly ridden. Some of those rides were on mountain bikes, so trails and gravel roads will be included. Cities have a lot more riders, so they show more red roads.
Here's the link to central and eastern Kansas. (As you pan and zoom the map, the URL changes, so you can bookmark that view.)
Heat Map Kansas
Click "
Toggle Labels" on the left side menu to show town and road names as you zoom in.
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Biking west to Colorado
It looks like the western part of Kansas has a small number of commonly ridden east-west roads.
I'm guessing that most of the other roads are gravel in the west half of Kansas. Zoom way in on google satellite view, and look for painted centerlines on the paved roads, and/or tar stripes on "chip-seal" gravel & tar roads. I often need to click "Labels off" on the left side pulldown menu, to see the road image itself without the google road overlay.