Pretty much any rate where you're assigned to a shore installation. Sailors at sea have little time to study for college, though it's a lot easier today than it used to be.
For example, Photographer's Mates, Musicians, Journalists, Corpsman, etc., are rates in which shore time can be more than sea time. However, the Navy is a seagoing service, and there are few jobs worth having in the Navy that aren't required aboard some type of ship. Even barbers are assigned to Navy ships.
What you might not realize though is that every training course you go through (including Boot Camp) has a college credit equivalent. Between my Navy courses and Civilian DoD courses, NASA courses and about 18 months of college credits, I'm only about a year or so from a BS degree as all of those courses in the Navy I took have college credits assigned to them.