The part of the sentence that is the nonrestrictive clause is the following one: "(...) which is free for all full-time faculty". Nonrestrictive relative clauses contain information that is not essential to understand the meaning of the sentence and therefore can be dropped without altering its meaning. If this test is applied and the sentence is still grammatically correct, then it is a nonrestrictive relative clause. What is more, they are introduced by relative pronouns (which, who, where, when).
The college cafeteria, which is free for all full-time faculty, is a popular and safe environment for students to study.
The college cafeteria is a popular and safe environment for students to study.