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I might be wrong, and I am sure some one will correct me, but I think that there is some dumb federal law about carrying concealed on a college campus or dorm.
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Generally applies only to elementary, middle, and high schools. The federal law you're referring to lets states define what "school" means for the purposes of this law.
I know in VA it is technically legal to carry at a private college if they don't prohibit it as a private property owner (otherwise your CHL is invalid under 18.2-308 (0) ), and it is always legal to carry at public ones UNLESS it is one of the ones that VA has a statute for (U of Richmond I think???).
I am prohibited from having firearms on campus at W&M, but it's only a college rule (not law). Ironically, someone who is NOT a student could carry here. Same deal at my undergrad school in PA. A guy on this board from VA Tech talked to his school's general counsel and was told it is legal, but a school violation for students while on campus.