Depends. Do you want a latin sandal-type shoe or a practice shoe (which is usually more like an oxford or tennis shoe in construction)? Your teacher may have a preference for which you wear to lessons.
It's hard to recommend a specific shoe. They all fit a bit differently and it's mostly trial and error to find the brand that works best for you.
To see a large selection of shoes, try backbaydancewear.com. In NYC, I've heard that Worldtone has a big selection, too, which you can try on since you're there.
My favorite practice-type shoe is the low-heeled Godiva by Elegance, which I got from dancehappy.com. It's pretty enough to wear for social dancing, too.
Welcome to dancing! Good luck on your shoe search.