A museum visit can be exhilarating, inspiring, but also, by turns, infuriating or just plain boring. This is particularly true when visiting one of the huge, all-encompassing institutions such as the Metropolitan or the Louvre. Smaller museums—such as the Frick or the Neue Galerie—demand less from us, intellectually and physically. The menu is more limited: the art on display often represents only one culture, one period, or even one medium. Indeed, who could deny the pleasure of a day spent at the Beyeler Foundation in Basel or the Clark Institute in Williamstown?

There are, however, museums created in yet another format: those that are of relatively limited size but are also encyclopedic in scope. Two of the best are about an hour’s train ride from Manhattan: the Princeton University Art Museum and the Yale University Art Gallery. Because they serve a primarily didactic purpose, their departments are equally as diverse and far ...

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