I'm not sure how long you will be staying, how many shows you want to see, or how you define "new." This season? Something you haven't seen?
But if you want to see Hello, Dolly, you should get tickets in advance. (I will probably regret not seeing it with Bette Midler in what sounds like a very good production.) dramarama611's list of new musicals are the critical and commercial hits of the season. I saw Dear Evan Hansen and Great Comet on a trip earlier this month, and liked both of them very much. Dear Evan Hansen tickets are ones to get in advance if possible. It's a tough ticket. You can wait on Great Comet, as seats are available now and might be easier to come by when Josh Groban, one of the stars, leaves the show in early July.
Money's no object? See Hamilton, if you haven't already seen it on tour in Chicago or San Francisco when you were visiting your aunt.
These are the obvious choices, the shows that have won or will win Tony Awards. There are other options that other folks can recommend. It depends on what appeals to you.