Interesting how Hy-Vee's entrance in the 1980s came by succeeding Geifman's. According to
this article, Hy-Vee didn't buy the company outright; rather, the Geifman family decided to exit the grocery business due to the economic toll of the farm crisis, sold their store locations, and reformed as a real estate management business.
Kroger had a spotty existence in the Quad Cities...a surprise to me, since they've continued to operate in nearby markets like Sterling, Illinois to this day! If the table is any indication, they entered the Illinois side (and not the Iowa side) by 1930, withdrew almost immediately, tentatively re-entered with single stores in Davenport and Moline in the 1960s, then left for good.
National had a presence until 1977, when Loblaws
cut off several of their American limbs to stem the bleeding at the head. The Iowa side didn't yield any good artifacts, but the Illinois side was better:
927 16th Ave in East Moline is now a Family Dollar, and has a pylon and an intact original entrance configuration. It also did time as an Aldi, oddly enough. Nowadays Aldi guts and re-facades any building it touches, but their practices were obviously different in the earliest stateside days of that chain.
1617 11th St in Rock Island doesn't have a pylon, but it's an almost 100%-intact 1960s supermarket building otherwise, with floor-to-ceiling windows and aluminum-edged canopy! Not surprisingly, it's also now a Family Dollar.