Oh oh oh Federal Hall, duh, heh. The whole memorial thing threw me - yes, there's an exhibit and stuff there and if you like history. I'm surprised he didn't add Grant's Tomb (he's there, really!).
I'm pretty sure you can do whatever tour appeals at the Tenement Museum. I don't think they like, ask for birth certificates or anything - just say he's 12 (this year) if they ask. I mean you can call and ask too but it's mostly just that the 12+ tours are longer and have discussion and more historical themes and all that younger kids may have a hard time following or not get engaged in and be bored by and possibly disruptive (just because if you're dragging the 6-year-old around for two hours while people talk about treatment of immigrants then and now, they can get whiny and antsy).
If he's mature enough to be interested in Federal Hall, I presume he'd be fine with any tour there.
Same as St. John I'd wager but you can call there too. I'd say he's 12 this year, just a few weeks after the trip or whatever (true) and see what they say but I don't think they ask for proof or anything either at all. If you're obviously lying they might question you but he's old enough to speak for himself articuately so it's not like you're trying to get an 8-year-old to pass, you know?
If you go there, be sure to check out the gardens outside. There be peacocks!
It's also right by (like a 2-minute walk) Columbia U, which is really an amazing campus. You walk in off Broadway and you're in an entirely different world.
There's also a Five Guys right by there, on B'way and I think...111th (Columbia is on B'way and 116, the Cathedral is like one block over from B'way and on 112 or so. I think Five Guys fries are gluten free and fresh from actual potatoes - they only fry fries in their fryers I *think.* Check their website if you're not familiar. They're AMAZING fries, heh.
As for the Chrysler Bldg. I don't think you can go in? I mean you can go in the lobby, and yes, it's pretty, the elevator thingys and all are deco and there's a mural deal but that's it. I've never heard of a tour or being able to go in the spire or anything.
The Whole Foods closest to where you're staying will be the one in the Time Warner thing at Columbus Circle. It's a NY experience, the place is like Calcutta, heh.
I mean it's fine, it's a Whole Foods, it's in a very snazzy shopping center thing (with the best restaurant in the City in it), but it gets crowds like no Whole Foods you've seen. The lines can be 75 people long, easy, but it moves quickly - they have (literally, they're numbered) 40 registers.
Big selection though, lots of everything. I also tend to see a lot of celebrities in that WF, if that's a thing for you. Recently Ronnie Wood, Howie Mandel and someone else I can't recall when I happened to be in there (at different times).
As for sports, there's also the Rangers.
You may also overlap with Comic Con, if he'd be into that. It's a HUGE event.
I'd definitely call about the dance class and the Costume Collection - taking a class in NY would be really cool I'd think and they'll be really nice I'm sure.
Oh, for stuff going on when you're here - check Time Out NY and NY Mag. They''re both online and both have extensive calendars of everything going on, especially stuff you may not think of, like off-B'way shows, little dance companies, exhibits, galleries, whatever. He can peruse to see if anything wacky catches his eye. There are a lot of free concerts - street fairs - lots of stuff.
There's still Rocky Horror that shows at the Waverly downtown, and movie houses that show classic stuff and fun stuff and etc. Check Time Out.
We just had Clock here, it's an art installation that's a movie that runs 24 hours and shows clips from films that show a clock every minute. So like, a clip where someone looks at their watch at 8:02, then different scenes, with people saying stuff like 'it's 8 o'clock already?!' then a clip panning a clock that says 8:03 - all timed to the actual time. It was silly and odd and just a free thing, you could walk up (and wait on line to get in if it was crowded) and go sit in the theatre and watch til you got bored. There are a lot of things like that.
Oh - someone mentioned the Planetarium having an extra fee - that and Natural History, like the Met Museum (and Cloisters, which is awesome too btw), are donation museums.
They have suggested admission prices, but will let you in for whatever you can give. The suggested donations are like $15 or $20, but if you hand them $5 or $2 or whatever and say 'one please' they will hand you a button showing you paid without comment or question.
The exception is tickets to the movies in the Planetarium and the nature IMAX movies (which are awesome) at Natural History. Those have ticket prices like any movie. Also the MOMA has an admission price, not a suggested donation, that you must pay to get in, though there are free admission evenings every week.
Make sure you are in the right lane though. Ask!! It was rather confusing. oops. I also saw that someone recommended skipping it. This is the Statue of Liberty. Not quite sure how a once in a Life Time trip to NYC is complete without a trip to the Statue. 
Thanks
