Fred,
In KC, I have played Tiffany Green (by the airport NW of city), by RTJII, and Iron Horse south in Leawood by Hurdzan. I have also toured Spring Hills (?) by Ken Dye, a city course near Olathe, and another one by Schreiner near 35 and 10 on the SW side, but within housing. All are good modern tracks.
DA Weibring also has a new one on the far NE side of KC, but I have not seen it.
As far as public classics in KC, Swope Park is a Tillie, much remodelled, I believe, but the routing is still there, to my knowledge.
If you have any connections, Tom Watson's home course is KC Country Club, and Mission CC (? exact name?) ane a few others in that area.
If you are willing to drive west to PD, you could also try to get on Fazio's Flint Hills in Wichita, and/or go to Manhattan to play my Colbert Hills, a public course you should have no trouble getting on.