Research: I've tried Googling various terms together: "ice rink" + "disney on ice" + "manhattan", and other various permutations. I've also tried going to ticketmaster and searching up Disney on Ice productions in the New York City/Tri-State area to look for venues.
I'm looking for venues for ice-skating productions like Disney on Ice, close to Manhattan - the closest one I can find is the Nassau Coliseum in Uniondale, but I'm looking for something closer to the city (not on Long Island), in walking/short cab ride distance from Central Park (if that's at all possible...)
ETA: Thanks so much for all the help, you guys are great :) All the suggestions were exactly what I was looking for! I will probably end up using Madison Square Garden. Thanks again!