Hello Rosemarianne !
I can see from your picture that your dog is a little bigger than mine !
There a a lot of hotels in the area of the city where the Montreal Port is. We have all the big ones (Delta, Holiday Inn, Mariott etc.). There are also some small local hotels or Bed and Breakfasts.
There are also a lot of metro stations nearby, so it depends on where you would like to stay:
If you arrive by train you will be near the cruise terminal in Old Montreal. The closest metro stations are Square-Victoria (closest to both the train station and cruise terminal) or Place d'Armes (a little further away). There is a lot to see there as you are in Old Montreal but you are not in the gay Village.
If you guys want to be close to the Village, the closest metro stations are Beaudry (in the Village) or Berri-UQAM (just outside the Village but closer to the Port and Old Montreal). You should know that Ste-Catherine street in the Village is closed to all vehicles and becomes a pedestrian street from May to September. Although this a great because there's a very festive atmosphere with all this activity, the dates for the cruise are a little early for this and they will most likely be setting everything up during the pre-cruise week. Just though you might like to know in case it would bother you.
So in summary, let me know what kind of hotel you would like and where you think you would like to stay and I can look something up for you or give you references where you could get the information you need.