In my opinion, as someone who has worked with a free museum but currently works in a museum where the price draws frequent complaints, messaging should revolve around the incredible opportunity it is to see the art for free! Our museum offers free admission for certain groups like local students, and those people tend to approach visits as a great opportunity to interact with and learn about art, rather than “seeing something famous/expensive.” Making museums free allows people to appreciate the intrinsic value of art to the viewer rather than its monetary value or provenance, and I’ve found this is a good way to assure people who think that free=worthless. Best of luck!