HR Hotel Booking?

My internship has us train at regional headquarters; we're flown in to HQ and they're putting us up in a hotel while we are at headquarters before we start for real in New York. They had everyone from CA/the west coast get in at about 7am on the day of the internship taking a redeye, so we all asked if we could get in the day earlier. They changed it without any issues. However, since they still haven't given us hotel information, we're not sure if the company will pay for the hotel this extra night or not.

A night at a hotel within a ~20 min walk is about $160 if it's NONREFUNDABLE, to schedule a cancellable hotel would be minimum $240. It's expensive to stay in NY and I'm not sure if I should bite the bullet and just pay the nonrefundable 160, or schedule the cancellable hotel. We are only about 3 weeks out from the internship start date, so I'm not sure why HR hasnt' given us our hotel assignment/details yet. If I keep waiting, I'm sure both prices will go up, but I don't want to waste $160 if HR will just pay nor do I want to pay $240 if I could pay $160. 

What are any suggestions? Because we do not know what time we're starting on day 1, I want to make sure I CAN walk to the office if necessary and not be reliant on Ubers/taxis. It's also in a financial area so all hotels are reasonably expensive unless I cross to the other side of a highway, which would also be ~30+ min walk.