Ice skating indoors: Atrium (near bonaventure central train station)
Ice skating outdoors: The old port by the Cirque du soleil tent
Tubing: not sure, haven't been since I were a kid in local parks
, but here's a link:
Montreal Snow Tubing Hills 2016-2017
Not sure about hotels in Montreal. But I would stay somewhere within walking distance to a metro (subway) station.
I would rent a car to go to Quebec City. It seems to be awash time-wise, likely cheaper and more convenient once you get there.