My neighbor E. moved here from Hungary w/ her twin boys this fall, and is on the lookout for engaging, mind-expanding adventures for them. I'm tossing my ideas for her here.
Adventure Aquarium (Camden, NJ) (Take the RiverLine light rail train!)
Cotsen Children's Library (Princeton, NJ)
Freecycle (Princeton, NJ) (Fun to scour the house for things ready for passing along, and also fun to keep an eye on the listserv postings for "treasures")
Howell Living History Farm (Lambertville, NJ)
Ice Land Skating (Hamilton, NJ)
Kelsey Theater (@ Mercer County Community College)
New Hope Train (New Hope, PA)
New Jersey State Museum (Trenton, NJ)
Off-Broadstreet Theater (Hopewell, NJ)
Princeton Parks (Princeton, NJ) (the one off of Lovers Lane has a particularly little kid-friendly giant sand pit)
Princeton Public Library's Kid Programs (Princeton, NJ)
Princeton University Art Museum (Princeton, NJ)
Ride the Dinky! (Princeton, NJ)
Terhune Orchards (Princeton, NJ)
Walk the Trails (Princeton & environs)
Westminster Conservatory Recitals (Princeton, NJ)
And, if don't mind ads, you can poke around PrincetonKIDS.
(Special thanks to @analomba for her great suggestions!)