I first went to the Papermill Playhouse on a field trip when I was a chaperone for my son's class trip. We went to see their production of It's a Wonderful Life and I have to say that it was absolutely marvelous. The theater itself was very nice, inside and out. The staff was very friendly and the actors were very professional.
There are shows and programs specifically for children and many of the season's shows are appropriate for children or older children as well. I believe there are student rate tickets sometimes (could have restrictions). There is a pretty brook outside the theater which adds charm Broadway doesn't have. The theater has parking lots (for a fee) and the town has lots of restaurants which would cater to children as well, such as Charlie Brown's, Pizzetta, and Sapporo to name a few.