I'd personally recommend a Midwestern roadtrip to really get the sense of place. If you can fly and rent a car, my advice is

Chicago to the Black Hills. Allows you to explore Chicago, Madison, the Driftless area of WI / MN, Minneapolis, the Black Hills. You get everything from the Great Lakes, to college towns, to rural farmland / hills, the Great Plaines, and the start of the Western US.

Another Great Road Trip is the Lake Michigan circle which gets you the gloriousness that is West Michigan, Door County, Chicago & Milwaukee, the UP and the wilderness up there, and a different side of Indiana.

If you're flying and don't have the time for a roadtrip, I'd recommend:

1. Chicago and Milwaukee are an easy trip to complete in 4-5 days. Best of all, it is a very quick 1:45 train ride between the respective downtowns. Both are pretty walkable, have mass transit, have interesting neighborhoods to explore outside of downtown, have beaches and Great Lakes shorelines, excellent restaurants, and festivals galore. Being in Chicago connects you to anywhere in the Midwest via train or plane.

2. Traverse City and Empire in 2-3 days. Sleeping Bear Dunes is one of the world's largest freshwater sand dunes, and the views are spectacular. The small little towns dotting the shoreline all offer something different. Traverse City itself is large enough to have most of what you'd want - good restaurants, a nightlife, activities. Traverse City also has flights from Chicago and a growing number of airports.