I'm not sure On The Town will still be playing when you get here. It's been playing to very low capacity for weeks and if they don't score big at the Tony noms I'm afraid this will be the next one closing.
I can highly recommend On The 20th Century, either as a substitute for On The Town or as one of your open slots. It's just an all around fantastic show, it's hilarious, beautiful for the show, great music you won't get out of your head and pretty much one of the best nights you can have on Broadway. It got rave reviews all around and it got them for a reason. It's also a limited run (currently scheduled through July 5 but I think likely to extend for a few weeks), so that will be your only chance to see it, too.
I've only heard wonderful things about Curious Incident, and it's high on my must-see list as well.
I also had a wonderful time at It Shoulda Been You, actually. The show is very unexpected, very funny and much better than you would might think from the description.
I don't know how often you come to New York, but Hamilton is likely to run for quite a while, and Something Rotten might as well if it's as good as everybody says (I have yet to see it, too many shows opening right now to keep up).