Monkey Bar, La Pecora Bianca (several locations in Manhattan), maybe Grande Boucherie or one of the other Boucherie locations, although if Balthazar is not of interest the menu there may not be either.
Don Angie is an extremely hard reservation, but people sometimes have good luck. You’ll have to log onto Resy right when the reservations for your date are released. Could also call/email and see if something is available. Bad Roman is a little flashy but very instagrammable and very fun. And has great cocktails! The small drawback is that it’s in a mall (the one on Columbus Circle) but if you are going before or after a show or something in Midtown it’s relatively close by.