University of Mississippi (Ole Miss) offers non-resident merit awards for those with an ACT score of 27 of $6,000 per year. Same applicant may be offered additional scholarships based upon certain factors such as STEM major, majoring in certain foreign languages, Eagle Scout, etc.
Also, check out Mississippi State University
https://www.admissions.msstate.edu/scholarships
College of Charleston non-resident merit scholarships of $8,000 - $12,000 per year for those with high school GPA of 3.80 and higher:
Wilkes Honors College of Florida Atlantic University scholarships (apply by Dec. 15th):
Rollins College Orlando, Florida area:
Berry College in Rome, Georgia
(Many more, but too busy to continue listing.)
P.S. What is your planned major ?