Copps Coliseum is a real hockey stadium, but although depicted as being in an unspecified U.S. city, it's actually in Hamilton, Ontario, Canada. The city skyline seen in front of the stadium fire at one point is that of Toronto.
The street chase, train station, and subway scenes were all shot in Toronto. All the subway stations depicted are actually the same unused platform. This is why the escalator is shown as dismantled for maintenance when the characters enter the station: it was removed when the platform was closed.
Mimi Kuzyk who played Eleanor Grayson was also Sam Beckett's wife in another time traveling series Quantum Leap (1989).
The street chase scene ends at Toronto's Union Station with the Monument To Multiculturalism (a statue of a man and birds) in front, which was unveiled on July 1, 1985.