Pacific Northwest - OR,WA,BC

I'm unfamiliar with these museums but I hope they see increased visitors on these days. I like the idea of pay what you can entry. Some in my area have a free admission day every few months or so, sometimes during the last week of an exhibit. Seems to work quite well.

Fun story, a few years back I had appointment rescheduled leaving me with a free day in Toronto so I decided to go walk around the Royal Ontario Museum. I managed to mix up the transit schedule and ended up there an hour before opening. Much to my surprise, there was already a line around the corner.

As I waited, loads and loads more people were arriving. I finally asked someone if it was always like this, and turns out I'd turned up on Family Day when they do free admission. The place was packed as far as the eye could see. I asked a staffer as I was leaving and they said it's their highest capacity day each year.