The hidden jewel of public courses in the Quad Cities is Glynn's Creek - Scott County (IA) Park - wooded, rolling, CHEAP. Fine example of keeping costs low while maintaining the course impeccably. The design itself is not full of thrills, but it's rock solid and a wonderful day's walk.
Hawthorne Ridge in Aledo, IL has some terrific holes, but maintenance was up and down over the years. Don't know how it is these days. It'd be a closer drive from Peoria.
Davenport's munis are pretty mundane - Emeis is the best of the bunch. Duck Creek is kept well, but also features a few of the unkind things some people really mean when they say "sporty".
Bettendorf has Palmer Hills. Fine, but not great. Worth visiting to see one of the truly awful (IMO) holes in golf - a par 5 that goes something like 5i/blind 3w/wedge.
On the private side, if Davenport CC doesn't happen, Crow Valley in Bettendorf and Short Hills in East Moline are very good golf courses. Also, Oakwood held the Hardees/QC Open/Classic/whatever for many years - it's an early Dye that many enjoy but I'm not very fond of it, frankly.
(The best "Golf" course in the quad cities may actually be the disc golf layout at West Lake in Davenport. How'd that land go to the "wrong" kind of golf
If someone would just loan me a mower and 18 pins...
)