Go to schools that have a good academic reputation for the majors you're considering. The name of a school can add extra worth to a degree and help make a strong Plan B. The name of an NROTC unit is worthless and will get you nothing.
As to Greek life, my NROTC my NROTC unit didn't condone or discourage it. If you wanted to go Greek, that was cool. If not, also cool. I'd say about 50% of my unit was Greek. Any unit, however, will expect you to prioritize NROTC over a Fraternity since Navy is paying your bills. But if you get good grades, do all your NROTC requirements, and still manage to be active in the Greek system, no one should care.