I would be VERY surprised if any college in the USA charges membership or per-use fees to full-time students.

I know none of the colleges near me does. (Two small independent four-year DIII liberal arts schools, two two-year schools, and two branch campuses of major universities.) They differ as to what, if any, facilities they make available to the public, and there's usually a charge for that. Alumni can usually keep their access either by joining the alumni association or by paying a membership fee.