Seems like everyone is telling you to go to western Michigan, I read it as you wanted to go to the western shore of Lake Michigan. There should be beaches all the way up WI's eastern coast. I know there is a beautiful white sand beach in Algoma, and nice beaches all up Door County. There probably are some farther south, too, but I haven't personally inspected to see.

Google Maps says Algoma is 5 hrs 57 minutes from Davenport.