Of the ones Ive been to, MOCA in Chicago and the CCAC in Cincinnati are great modern art museums. CCAC is more of a Kunsthalle, but the shows are quite good. MOCA has a great collection.
Art Institute of Chicago is probably tops for "The Art of the Museums"...old masters, modern classics etc.
For technology musuems that work for adults as well as kids, the Youngstown Musuem of Labor & Industry and the Henry Ford Museum are great.
For local/state history the Indiana State Museum in Indy and the Heinz Regional History Center in Pittsburgh are excellent.
For smaller local history mueums would be the history museum complex in South Bend, which incorporates an excellent newer museum, an industrialists mansion, and a factory workers house. For a smaller city this is a great little complex.
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