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Assuming you are talking approximate center of each state (Minneapolis MN and Richmond Virginia) the closest major city to half way would be Indianapolis Indiana.
If you are talking driving distance and the fastest route The closest major city to the halfway point is Indianapolis IN. According to Google Maps the distance is 1209 miles. The distance to Indianapolis is 620 miles.
The halfway point between Virginia, Minnesota and Springfield, Illinois is Coon Valley, Wisconsin. These hotels are within a 16-mile or less radius of Coon Valley:
Westby House Victorian Inn
Americinn West Salem
Holiday Inn Hotel & Suites La Crosse
Courtyard by Marriott La Crosse
Baymont Inn & Suites La Crosse/Onalaska
Microtel Inn La Crosse Onalask
Radisson Hotel La Crosse
GrandStay Residential Suites La Crosse
Candlewood Suites La Crosse
Stoney Creek Inn
Holiday Inn Express Onalaska
Hampton Inn
Comfort Inn Onalaska
Super 8 Motel - La Crosse
Brookstone Inn
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