Quad Cities to Mendota should be about 1.5 hours...maybe a few minutes more or less...
Lake Kakusha is in Mendota, but I don't know about the ice on it....it is a public lake. With all this snow, they might not have plowed the access road to the lake, but if you do a mapquest check on mendota and find Kakusha at the northwest edge of town, you can find a city street near the south end of the lake that borders a park and access there....snow will be deep walking in though.
LOL...sounds like some kind of scavanger hunt....