Fred,
You didn't mention exactly what days you would be in town. But, here are a couple of suggestions other than the normal tourist stuff.
Carolline's on Broadway is closing up for good and the last shows will be on New Year's Eve. Leading up to that, Dave Attell will be doing his normal week of shows between Christmas and New Year. He always gets some notable comedy luminaries stopping by. With Caroline's closing down, these shows should attract some notable comics. Your son can attend along with you. But, some of the material could be a bit raunchy.
Since you are going to be in Brooklyn, Patti Smith and her Band are going to be at
Brooklyn Steel in Williamsburg on December 29 & 30. The shows are listed as 16 & Over.