In reading more about what you wanted in a college, the first school that popped into my head was Tulane. It’s in the south, it has an academically strong student body, and it’s had quite a year on the gridiron. If you’re interested in Tulane then you will really need to show them how interested you are…they want kids who really are excited about Tulane. It’s not a guarantee, but I think you’d stand a decent shot at sufficient merit to bring the cost under $50k.
The next school I thought about was U. of Miami. Again, warm weather, an academically strong student body, a storied football program, and it’s one of the most generous schools with merit aid amongst the Top X schools. Again, no guarantees, but I think you’d have a respectable shot at getting this into budget.
Not a football powerhouse and not in a warm location, but Case Western can also be very generous with merit aid (relative to other Top X schools) and there’s lots to do in Cleveland. This is another school that wants to know you’re really interested in it; Case does not want to be a backup to a higher-ranked Top X school and it’s not afraid to defer or reject students that view it that way, no matter how impressive the resume.
If a strong honors program works for you, then you may want to consider U. of Arizona in Tucson or U. of South Carolina in the state capital of Columbia. You would definitely a lot of merit aid from U. of Arizona and you would probably receive a lot from U. of SC. Another possibility would be U. of South Florida in Tampa or U. of Central Florida in Orlando. I’d be beyond shocked if you didn’t get an out-of-state waiver (which would bring tuition, room & board to $19k/year), and quite possibly more merit aid beyond that.
U. of San Diego is the last school that I’m thinking of for you. No big football here, but strong programs in one of the best climates in the U.S., and I think you’d stand a good chance at getting sufficient merit to bring the price within budget.
And if you love LSU football, have you thought about LSU? There’s an honors college and it is its state flagship…
Almost all of these programs are also ABET-accredited for industrial engineering or systems engineering, should @aquapt’s recommendation be of interest. And all these schools are ABET-accredited for various engineering specialties.