http://automaticfulltuition.yolasite.com/
http://competitivefulltuition.yolasite.com/
https://www.kiplinger.com/tool/college/T014-S001-kiplinger-s-best-values-in-private-colleges/index.php
https://www.kiplinger.com/tool/college/T014-S001-kiplinger-s-best-values-in-private-colleges/index.php?table=lib_arts
(Click-sort on the two columns labelled “non-need-based aid”; related information also is shown in each school’s Common Data Set, section H2A)
All the above information sometimes is out-of-date by the time you see it. For any schools that interest you, check the individual college websites for the latest available information.
Of the colleges granting large merit awards (full tuition/ full ride) automatically for qualifying stats, Alabama seems to be one of the highest-ranked. Many of the most selective/prestigious schools (Ivies etc.) focus more on need-based aid and offer little or no merit money. There are exceptions, such as the large (and extremely competitive) Robertson scholarship at Duke and UNC-CH. Vanderbilt is a prestigious private university that seems to offer relatively large amounts of merit money.
UMCP has the Banneker Key scholarship program, but the biggest awards go to very few students. Colorado has the Boettcher Scholarship program, but it is limited to Colorado residents attending colleges in Colorado. You may want to check if your own state, or public universities in your state, have similar programs.