It may not be the classiest rink in the city, but I highly recommend heading down to Pier 17, South Street Seaport, and taking a few laps around Seaport Ice! It’s way cheap ($5 for admission, $7 for rental). We were there last night, a Saturday night, and there were hardly any people on the ice. It was a blast! Plus, there’s no time limit! You can’t say all that about the big boys: Bryant Park and Rockefeller Center.
P.S. I also recommend Lasker Park at the top of Central Park, which we went to last year and enjoyed, as well!