Philadelphia is a relatively short train ride away. I think it's about 75 minutes on Amtrak. I live in South Jersey just outside of Philly and look at NYC as very close by, getting in a few tikes a month.
Philadelphia is an amazing city, especially if you are visiting the US. It's the birthplace of our nation. There are lots of great historical sites and museums and some amazing restaurants.
Not sure when you are planning to come stateside. I'm guessing at this point you are looking to 2021. Tour wise we are meant to have Ain't Too Proud in March, Oklahoma in May, The Lion King in June and Hadestown in July. ATP, Lion King, and Hadestown will all be playing the Academy of Music. It's not an ideal venue for musicals, but it is a gorgeous opera house, one of oldest (if the oldest) still working opera houses in the country. Oklahoma will be at the Forrest, which is a quintessential road house, designed just like a Broadway house. It hosted many an out of town tryout in the Golden Age, Funny Girl and Chicago amongst them.
We also have Walnut Street Theatre, which is the oldest still operating theatre in the country. Their productions (all Equity with occasional NY talent) can be hit or miss, but usually are worthwhile. Next year they are meant to have Blithe Spirit, Death of a Salesman, and On Your Feet. Though that could change depending on how their fall lineup pans out. The Arden Theatre in Old City is also fantastic.
In April, our world renowned orchestra will be performing South Pacific, plus the great Yannick Nezet Seguin will be conducting La Boheme in May.
It's a great city, with many arts options. Highly recommend coming down when you visit!