Many of the state public schools have automatic merit aid for certain SAT or ACT and GPA. Here are links to the ones I could find. I’m sure there are more out there but thought this might be helpful.
Arizona State University https://scholarships.asu.edu/estimator
Auburn University http://auburn.edu/scholarship/undergraduate/freshman.html
Boise State University https://financialaid.boisestate.edu/scholarships/non-resident-tuition-assistance-programs/
Clemson University https://www.clemson.edu/financial-aid/types/scholarships/clemson-scholarship-recruiting.html
Colorado School of Mines https://finaid.mines.edu/scholarships/
Colorado State University https://financialaid.colostate.edu/scholarships-for-entering-non-resident-freshman/
Florida Gulf Coast University https://www2.fgcu.edu/Admissions/Prospective/scholarship.html
Iowa State University https://www.admissions.iastate.edu/scholarships/freshman_award_calc.php
James Madison University http://www.jmu.edu/admissions/apply/scholarships-mas.shtml
Kent State University https://www.kent.edu/admissions/undergraduate/new-freshmen-scholarships
LSU http://catalog.lsu.edu/content.php?catoid=16&navoid=1263#Entering_Freshman_Nonresident_Scholarship_Programs
Lynchburg College https://www.lynchburg.edu/admission/financial-aid/types-of-aid/freshman-scholarships/freshman-academic-scholarships/
Marymount University https://www.marymount.edu/Admissions/Financial-Aid/Types-of-Aid/Undergraduate/Scholarships
McDaniel College https://www.mcdaniel.edu/undergraduate/admissions/apply/merit-scholarships
Miami University http://miamioh.edu/admission/merit-grid/index.html
Michigan State University https://admissions.msu.edu/cost-aid/merit-based-aid/freshman/out-of-state.aspx
Millersville University https://www.millersville.edu/finaid/grantsscholarship/admissions-scholarships.php
Mississippi State University https://www.admissions.msstate.edu/freshmen/money-matters/scholarships/academic-scholarships/
Mount St. Mary’s University http://msmary.edu/admissions/financial-aid/scholarships-grants/index.html
New College of Florida https://www.ncf.edu/admissions/cost-and-aid/scholarships/florida-freshmen/
Quinnipiac University https://www.qu.edu/tuition-financial-aid/scholarships.html
Roanoke College https://www.roanoke.edu/admissions/scholarships_and_financial_aid/how_do_i_pay_for_college/merit-based_aid
Shippensburg University https://www.ship.edu/financial_aid/scholarships/scholarships/
Slippery Rock University http://www.sru.edu/admissions/financial-aid/types-of-aid/scholarships/first-year-scholarships
St. Mary’s College of MD http://www.smcm.edu/financialaid/types/scholarships/
Texas A&M University https://scholarships.tamu.edu/FRESHMEN/University-Scholarships#0-AcademicScholarships
The Ohio State University http://undergrad.osu.edu/cost-and-aid/merit-based-scholarships
University of Alabama https://scholarships.ua.edu/types/out-of-state.php
University of Alabama-Birmingham https://www.uab.edu/students/paying-for-college/scholarships/act-gpa-based-scholarships-out-of-state
University of Arizona https://financialaid.arizona.edu/types-of-aid/scholarships/freshman-transfer
University of Arkansas https://catalog.uark.edu/undergraduatecatalog/financialaidandscholarships/scholarshipsfornewstudents/
University of Colorado https://www.colorado.edu/scholarships/auto-consider/freshmen
University of Connecticut http://admissions.uconn.edu/cost-aid/scholarship
University of Delaware http://www.udel.edu/apply/undergraduate-admissions/financing-your-degree/
University of Georgia https://www.admissions.uga.edu/scholarships/
University of Idaho https://www.uidaho.edu/financial-aid/scholarships/out-of-state
University of Iowa https://admissions.uiowa.edu/finances/scholarships-first-year-students
University of Kansas https://admissions.ku.edu/tuition-scholarship/freshman
University of Kentucky https://www.uky.edu/financialaid/scholarship-incoming-freshmen
University of Louisville https://louisville.edu/admissions/cost-aid/scholarships/national-scholars-program
University of Maine https://go.umaine.edu/apply/scholarships/flagship-match/
University of Mississippi https://finaid.olemiss.edu/scholarships/
University of Nebraska https://admissions.unl.edu/cost/#scholarships/O
University of Nevada, Las Vegas https://www.unlv.edu/finaid/scholarships-freshmen
University of New Hampshire https://admissions.unh.edu/merit-scholarships
University of North Florida http://www.unf.edu/admissions/scholarships/Freshman_Merit_Scholarships.aspx
University of Oklahoma http://www.ou.edu/content/admissions/affordability/scholarships.html
University of Oregon https://financialaid.uoregon.edu/scholarships_freshmen
University of Pittsburgh https://oafa.pitt.edu/financialaid/academic-scholarships/university-scholarships/
University of South Carolina https://sc.edu/about/offices_and_divisions/undergraduate_admissions/tuition_scholarships/scholarships/nonresidents/index.php
University of South Florida http://www.usf.edu/admissions/freshmen/admissions-scholarships/nonflorida.aspx
University of Tennessee https://onestop.utk.edu/scholarships/volunteer/
University of West Florida https://uwf.edu/admissions/undergraduate/cost-and-financial-aid/awards-and-scholarships/freshmen/
University of Wyoming http://www.uwyo.edu/admissions/scholarships/non-residents/rms.html
Ursinus College https://www.ursinus.edu/offices/scholarships-and-financial-aid/grants-scholarships-loans/
Virginia Commonwealth University https://www.vcu.edu/admissions/paying-for-college/scholarships/
West Virginia University https://financialaid.wvu.edu/home/scholarships/freshmen/non-residents#Scholarship%20of%20Distinction%20Level%202%20NR
Western Michigan University https://wmich.edu/admissions/freshmen/cost-scholarships/scholarships
Winthrop University https://www.winthrop.edu/finaid/academicscholarships/