I believe that if you're with the 17 year-old, you can all attend a taping of the Colbert Report and/or the Daily Show, which they do Monday-Thursday. They're fun and free! They take up most of an afternoon, and you won't be able to see a show that night, but it's a cool experience. To get tickets to either, monitor this twitter page:
https://twitter.com/#!/DailyTix until you see ones come up for the day you want, and then act fast.
In terms of shows, I'd recommend Peter & the Starcatcher for sure, and also One Man, Two Guvnors. It was 30% off at TKTS today, but I think it was 40% or 50% last night. I'd also recommend Once and Newsies, but they're much more difficult to get discount tickets to.
I don't know how the One Man, Two Guvnors rush has been recently (i.e. since the Tonys), but I got there at 9 the week before the Tonys and had no trouble getting a ticket, so that's worth considering also.
Updated On: 6/21/12 at 10:57 PM