IMHO, it just depends on who else might plan to go at the same time you do. PI is a collection of clubs/bars. People drink alcoholic beverages inside the clubs and on the streets. Some people do things when drunk that you may not want your children to see. Some nights end up PG and others end up XXX. The problem is that you really cannot predict how any particular night might turn out . If you go early in the evening, you will probably run into far less of the "objectionable" behavior.
Many teens enjoy the Comedy Club (improv based on audience input - similar to the TV show "Whose Line is it?") as well as the Adventurers Club. No one under 21 is admitted to BET and Mannikins, even if accompanied by parents. (Those under 18 must be accompanied by a parent or guardian).
Best wishes -