For those who have never heard of a Children's Museum before, there is a national association in the US with some information. The basic idea stems from Vygotsky-like paradigms of learning through play.
My first impulse was: write a GUI that presents a series of standard cognitive tests in a fun way, put the software on a computer in a kiosk during the museum events. Finally, compare child performance on the test to the number of visits to children's museum.
Of course, there's some considerations: if somebody takes the test multiple times, they're probably going to get better at it, so this might give a false-positive (rising with the number of visits). So, for instance, only the first test taken by each person would be considered for analysis.
But that is a rather inexperienced shot in the dark. Any other ideas?