You can use BF at U of Miami, or most other Florida private colleges/universities. It would pay out based on the average public university tuition rate (about $6K a year for full BF) but then other scholarships/grants may come into play, such as the Florida Student Assistance Grant Program.
It may be worth playing around with UM’s net price calculator.
https://finaid.miami.edu/cost/index.html
If he’s interested in Engineering, you can use the ASEE college profile to get more info on each engineering program.
For example, “Enrollment by Class” will give you a sense of how many other engineering students are enrolled in the program, and what majors are offered. For example, UM has a large Industrial Engineering program, something you may not find at several other schools (like Alabama and Embry Riddle).