There are a lot of kid-friendly shows, including:
Newsies (read my Broadway review here)
Kinky Boots (oddly, I've heard it's child friendly)
Matilda the Musical (read my Broadway review here - I LOVED this show)
Motown the Musical
Phantom of the Opera
If you're not already an SHN subscriber you can get a season membership starting March 7 starting at 10 a.m. Otherwise, individual tickets will be available later.