A number of ice skating rinks open in Japan over the colder months, and one of the biggest in Tokyo is located at the Tokyo Midtown complex. The rink here has been in operation for 13 years now, and it's seen by many as one of the city's best winter traditions.
The event typically runs from mid-November through until late February, and after dark the area around the rink is illuminated to create a fun and festive atmosphere.
As for watching, I don't think there's any issue/fee with doing that, although it's not specifically stated so I can't say 110%.