Before I reset it was on the right which took a little getting used to (since I used to play on my brother's town and his was on the left), but in my current town its on the left.
It depends on your beach if it extends at the left or right. If your beach is extended to the left side, then your museum is at the right. If your beach is extended to the right side, then your museum is at the left.
My museum in my main town is at the right. And my OYC town is at the left
It's on the right. I doubt I could ever get used to it being on the left. In fact, I didn't even know it could be on the left until I encountered it in someone's town. I was so confused. Pretty neat that they decided to do that, though. Makes sense.