@Charmaine M.
Hi! I had a long reply to you that for some reason, did not post. That gave me time to reconsider what I posted before.
Ask yourself, why do I want to work at a property management company? What kind of real estate are you most interested in? Make sure you align your goals with that company.
I've worked for my family's management company, a big juggernaut property management company, and for myself. If you are strictly looking to learn about property management, there are lots of good firms in NYC near you. Do some research about what people are saying about the company online, check out employee reviews on sites like Glassdoor.
Warning: When property management is going well, there is usually nothing to talk about or review. You will run into good companies with no reviews.
Check out their websites and connect with the most junior employee you can find and talk with them. Like any good real estate investor, look at the properties they manage, find the owner and call them directly and ask how it is going.
It sounds silly, but find out what management software they use. If it is Yardi or something similar, you may spend your first four months learning only how to use Yardi (stuff of nightmares). Big value if your only goal is work for a property management firm.
If you want to learn a little about property management and real estate in general, find a medium sized real estate investor who has a property management division. That way, you get the most exposure to real estate deals and transactions and you might find that property management is or is not your thing.