If you have culturepass (free museum entry through your library card), you can also visit wollman rink in Central Park for free! You just have to search and book dates in advance because it can sometimes be booked out.
It still costs money to rent skates and for the locker rental, but the actual skating admission is free. It’s such an iconic way to experience the city and the ice is much better than Bryant park.
See more details and to book ahead of time here:
NYC Ice Skating | Iconic Wollman Rink in...