We went up there (and to Quebec City) in July, a very good time.
There's an on-off bus tour from Gray Line that's pretty good, we had a pass that allowed us to do it for 2 days. Stops off at several places, has a tour guide, and buses run fairly often (I think every 15 minutes or so, you can get on anytime with your pass/bracelet; but that may be times during peak summer times). Was great for a "taste" of many things, and we often stopped for a couple hours at various spots.
We went to the Chihuly Glass exhibit at the art museum, was pretty amazing, not sure if still there (edit: there through October 20th per web site). The Notre Dame Church and Church at Mont-Royal if you're into that (even as a Jew who's not a big sightseer, I was interested in both). Walking street near old town waterfront was fun, some decent restaurants and touristy shops. We didn't go to Swartz's Deli but to another place for the smoked meat - which was corned beef as we know it in US. Well done, and tasty for sure, but I was a little underwhelmed based on flowery descriptions I had heard previously.
We even enjoyed a local farmer's market (huge) in one of the neighborhoods.