The top 30 schools in the US by “research expenditures” are relevant to OP’s decision as Michigan, UPenn, UNC, Duke, USC, and Emory are included in this group.
Each year Johns Hopkins leads the nation followed by Michigan.
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JHU (Johns Hopkins University)
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University of Michigan
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UC-San Francisco
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UPenn
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Univ. of Washington
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Wisconsin
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Duke
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Harvard
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Stanford
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Univ. of North Carolina (UNC)
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Cornell
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MIT
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Yale
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Univ. of Pittsburgh
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Minnesota
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NYU
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Texas A&M
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Columbia
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Ohio State
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Penn State
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Georgia Tech
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Univ. of Florida
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UCal-Berkeley
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USC (Univ. of Southern California)
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WashUStL
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Northwestern University
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Vanderbilt University
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Michigan State
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Rutgers
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Emory University
This list includes both private & federal government funded research.
According to US News, there are 399 institutions classified as National Universities in the US. (211 public, 180 private, & 8 for-profit.)
Also according to US News, there are 223 LACs (liberal arts colleges) in the US (199 private & 24 public).