The Band's Visit is spectacular, and there are consistently very cheap tickets on Stubhub. (Many times less expensive than rush would be)
I'd suggest either My Fair Lady of Carousel, and have it up to you which show you like better. The cast of Carousel is genius, while the creative team behind My Fair Lady is just asking for it to be a gorgeous production. They are equal in my book.
I'd also suggest Spongebob and The Play that goes Wrong. Neither are great theater, but both are a totally fun evening.
In terms or straight plays, I'm mostly looking forward to The Iceman Cometh and Angles in America, although price is an issue for both, as well as Angles in America being two parts, and The Iceman being nearly 4 hours.