Is there a GPL license type that permits non-direct revenue (from the asset), such as the entrance fee for a museum? Or educational tuition?
The CC BY-NC 2.0 license regulates commercial exploitation in 4(b):
You may not exercise any of the rights granted to You in Section 3 above in any manner that is primarily intended for or directed toward commercial advantage or private monetary compensation. The exchange of the Work for other copyrighted works by means of digital file-sharing or otherwise shall not be considered to be intended for or directed toward commercial advantage or private monetary compensation, provided there is no payment of any monetary compensation in connection with the exchange of copyrighted works
The first sentence may allow the kind of use that you're describing, since The Work could be made available for money, but not for commercial advantage (which I take to be code for "profit") or private monetary compensation (code for "personal gain"). The second sentence addresses exchanging The Work for Something Else Copyrighted, so would not appear to be relevant to anything that you could do in a museum. (It does, however, say that there can't be any monetary compensation, so if you put the stuff on a DVD, you can't recoup your materials cost, though you can require an exchange DVD).
In case the work in question is music, (d) and (e) are relevant, the Licensor (creator) asserts the right to collect public performance royalties in case the primary purpose is "commercial advantage or private monetary compensation". This mildly contradicts what 4 restricts. This is just crazy, but required by law, because US Copyright law already has the concept of "compulsory license". The importance of that is that if the law allows X, the license cannot disallow X. 17 USC 115 compels the copyright holder to license nondramatic musical works under certain conditions, so the seemingly contradictory language pertaining to music just mirrors the situation with the law. It would have been a bit clearer if they had included the phrase "The restrictions in section 4 notwithstanding".
Copyright law already contains a limit on the copyright holder's ability to limit the work, with respect to public performances and displays (17 USC 110). The law allows
performance or display of a work by instructors or pupils in the course of face-to-face teaching activities of a nonprofit educational institution, in a classroom or similar place devoted to instruction
(It is best to read the whole thing to see how much is applicable to the situation in question). So even with a blanket ban on collecting money, there is still statutory permission for non-profit educational performance / display. The combination of what the law says and a generic non-commercial license may accomplish what you want. (Really, figuring out what you're trying to do is most important, and while you maybe should ask a lawyer to draft something for you, don't waste your time and money until you have a clear idea of what you're trying to accomplish).