I’d rule Vandy out. That kind of debt is not worth taking on for a school name. That leaves Rhodes and UMiami. Normally I’d say go with the higher-ranked/more prestigious one, which would obviously be UMiami. But you’re looking at fields where prestige of undergraduate name overall doesn’t matter a lot - although individual programs’ prestige within the field may matter. What is your intended major for undergrad?
Personally I’d go with Rhodes, very solid liberal arts college in a great city. But more information about your major/career choice could change that answer.
You said UMiami would cost 7k more - is that per year or over four years? Would you pay or your parents?