I think free is better than prestige.
Employers are going to be impressed that you got the scholarship.
Consider University of Alabama. You would be eligible for a Presidential Scholarship at over $107,000. What you don’t spend on undergrad they let you roll over into law or graduate school there. Sweet deal.
You only need to get a 3.0 to keep the scholarship. http://scholarships.ua.edu/types/out-of-state.html
Presidential scholars at any big state flagship get a lot of special handling and networking opportunities - chances to hobnob with big university admin and alums, internships, early registration, basically treated like the state’s royalty.