Families, you may wish to check out http://www.schooltix.com/ . They offer some reduced tickets to selected Broadway and Off-Broadway shows….
Local newspapers also post listings of upcoming community theater productions. For instance, you can see listings from the Queens Chronicle at http://www.qchron.com/qboro/stories/
There are lots of arts offerings in our NYC parks during the summer months….. check out http://www.nycgovparks.org/events/theater or http://www.cityparksfoundation.org/ The schedule for cityparksfoundation’s SummerstageKids is at http://www.cityparksfoundation.org/arts/summerstage-kids
You may also want to check out the performing arts centers of our local colleges, like Queens College & Queensborough, as well as Flushing Town Hall and Queens Theatre in the Park.