by peakhope
I am curious about this as well. Like you, I immediately thought that stopping at every location might maximize your points.There are 2 cases I can see where getting there first gives you an advantage:
1. At the inns, you get first choice of which menu item to buy.
2. Whoever completes each panorama first gets a bonus.
Neither of those seems strong enough to overcome all the "most of" bonuses that would be easier to get if you stop everywhere.