As far as I am aware, the only directly applicable Canon is 1221: "Entry to a church is to be free and gratuitous during the time of sacred celebrations." In other words, you can't charge a fee for the Liturgy. The commentary adds the following:
This rule, which follows from the right of the faithful to go to a church (c. 1214), applies to all liturgical celebrations. It does not apply at times when no liturgical celebrations are occurring, including special events, such as concerts, held in a church. In some churches of great historic or artisitic value a small fee is charged to tourists. Where that is the case, provision should be made for the free entry, at least for some period each day, of those who wish to pray before the blessed sacrament (cf. c. 937).
Two footnotes are found in the commentary paragraph. The first notes, "A suggestion to make admission to churches free at all times was deliberately rejected in the code revision process." The second notes a letter from the Congregation for Divine Worship and the Discipline of the Sacraments that suggested admission to concerts should be free, but left the decision to the ordinary.
I believe that this (from the Adoremus website) is probably the letter from the CDWDS. In the case of a church like St. Augustine, I believe that two ordinaries might be involved: the Archbishop of the Cincinnati Archdiocese and head of the Missionaries of the Precious Blood.