I haven't been personally, but The Filling Station in Davenport is supposed to be very good. I hear nothing but great things from family and friends that have gone.
The other one is Whitey's Ice Cream. It's no big secret in the QC, but if you're talking to someone not from the QC they kind of dumb-awed "WTF???" look on their face, however, several travel mags have rated Whitey's among the best ice cream on the planet.
Can't agree more about Whitey's. One of the two things I miss the most about the Quad Cities, the other being the Bier Stubbe in D'port. Hy-Vee carries the quarts so I can still get my fix of Whitey's at least.