Spiritual Meaning:
The past is a learning tool that can be observed at some length, and a museum, like a library, is a place where knowledge and expertise can be accessed and given due reverence. Gaining spiritual knowledge in particular allows us to progress.
Psychological / Emotional Perspective:
A museum can represent a place where we store our memories and,  therefore, can represent the subconscious – it is that part of ourselves that we will usually only approach in an effort to understand who we are and where we came from.

Everyday Material Aspects:
A museum in a dream denotes old-fashioned thoughts, concepts and ideas. We may need to consider such things but perhaps more objectively than subjectively.

You might also like to consult the entry for Old.