If it's dinosaurs you seek, look no further than America's oldest natural history museum (which, since 2011, has been run under the auspices of Drexel University). More than a dozen impressive specimens, including a massive T-Rex with jaws agape, are on display in the main hall. On weekends, kids can even "dig" for fossils.
(Fun fact: The Academy's bones of a Hadrosaurus, found in Haddonfield, New Jersey, in the 1830s, were the first ever officially attributed to having come from a "dinosaur.") The Academy is also home to dioramas featuring enormous moose, bison, and bears; a second floor filled with Asian and African flora and fauna; a tropical butterfly exhibit; and "Outside In," where kids can touch and learn about whatever animals happen to stop by that day.
Those animals—and those used in the stage shows—are mostly rescues kept in the Live Animal Center, which is now wonderfully visible behind glass on the ground floor by the 19th Street entrance (it used to be stuck, woefully out of public view, down in the basement back when I was a volunteer here in high school).