The best method/source I can think of is to become an IMLS GOS
grant reviewer. While you cannot use the information as it pertains to a
specific institution, a few years of reviewing grants will give you a good sense
of what's what with similar institutions. A question for IMLS would be whether
one could use the statistical information with identifiers removed for your self
study comparison. That is could you say X size museum in X size
northeastern city with a collection size of X does this and
that.