Do join a fraternity. I never thought of myself as the fraternity type, but joined one in my third year of college too after a few friends did. Best decision I ever made. 14 years later it's still a major part of my social life, both with current students and alumni from all years from my class to the present.

What a fraternity gives as opposed to clubs is the opportunity for unstructured types of social interaction. A fraternity house is where you can just hang out with whoever's around, rather than being always oriented on the tasks and projects of a club.

I wasn't the same guy after college as after high school, a change almost entirely induced by the fraternity. A Greek house is a fantastic opportunity to learn open-ended leadership roles and break out of the task-assignment structure of academia and business grunt work.

Whether commuting can work depends a lot on the particular fraternity, of course. Mine has always had a fair few commuters. It's not quite the same as living in the house, but with effort to show up and be around and involved, commuters can get a pretty good experience as well. It's not too late to join. The relationships and experience will stay with you after graduation.