This may seem depressing at first, but museums do a lot better than colleges/universities and hospitals on this question.
"Charity" simply isn't a word that people tend to associate with museums. While museums may legally be considered charities, I suspect the broader population defines "charity" much more narrowly.
But it does make me want to understand how certain words may make sense to the broader population, and others create dissonance, when thinking of "museums." Especially when thinking about museums and their impact.
A quick data tidbit from my recent studies. Far more to come!