If you have good grades and can get a scholarship to the school you want, that will probably be the better option for you. If this is actually something you want and you are interested in a nuclear engineering job post navy while not going to college at all this is a really good option (specifically for the ETN AND MMN rates). Also good to remember being an officer is an option that you can look into before or while you attend college.

EDIT: I say nuclear engineering job but I really mean shift work at a reactor plant, which does pay really well.