Oh wow, like many here I never knew it could be on different sides. Mine is on the left, I prefer an east coast town, as I'm from the east coast of the UK!!
I have it in the left in one of my towns and right in the other. Aesthetically speaking, I like it on the left side more but it seems more convenient on the right side since I don't go into the other shops on the left very often.
I always had mine in the right, this is why I get confused and ran to the right when I visited people's town whereas their museum on the left LOL!! hopefully they don't think I am being suspicious and flip the switch ;_;