Sounds like a fun roadtrip, I live in Des Moines and have never been to the Machine Shed, a lot of people go there and seem to like it, family style eating. I believe they also have a location in the Davenport area.
There are a couple of good tenderloin places in town, If your taste runs to that, try Smittys, good tenderloin sandwich (reviewed on RF). I like Big Tomato Pizza, lots of varied toppings and odd toppings(spam, corn etc) are available along with the usual, thats takeout only. Some good medium priced steakhouses, Iowa Beef Steakhouse is a cook your own, the cuts are good, the sides mediocre. Good restaurant up the street from Machine Shed is Sam&Gabes, they serve primarily Italian, kind of upscale. Lots of small neighborhood places, If you want to try something specific, please feel free to ask and I’ll try to answer.
Some place you may consider for breakfast is the Hamburg Inn in Iowa City about an hour west of Davenport. It’s a hole in the wall University town diner, been there forever. I always get the Reuben omelot whomefries.
Let me know If you have any questions about Iowa Places.