As a New Yorker, I have 2 questions about the center of the galaxy:
Is it open all night?
How far is it from midtown?
Is it open all night?
As a New Yorker myself, I think I can answer this:
Given that the galactic center is located in Sagittarius, and Sagittarius is currently rising in the New York City area around 3pm, and setting around midnight, it is not open (visible to us) all night.
How far is it from midtown?
About 26,000 light years (26,000 x 6 trillion miles).
Luckily, there is a very bright, white, star-like object in or near Sagittarius at this time. It's not actually a star, but rather the planet Jupiter, currently some 375 million miles from Earth. Perhaps you can stop off there along the way and use the restroom or grab a bite to eat. :)