More can be written on this, but you might be interested in a cabinet of curiosities labelled "The First Museums" in the FAQ. A couple of them ("When did the concept of a museum become a common thing?" by /u/past_is_prologue and 'What is the earliest example of what we could consider a "museum"?' by /u/TokyoBayRay ) have a little discussion on the very definition of "museum", which would affect your answer. There are a number of examples and explanations of the development of musea.

This is not to discourage discussion. Further questions, data, and debate are always welcome.