My wife and I were in Montreal for a few days in September. Had a great time. I hope the weather is good for you, because we spent most of our trip walking around the different neighborhoods and parks.
In terms of restaurants, we absolutely loved Au Pied du Cochon on Rue Duluth. It's probably not the best choice for vegetarians and likely impossible for vegans, so keep that in mind. It's very popular, so you'll need a reservation. Whether you try it or not, Duluth is a great street for wandering--lots of bars, restaurants, cool stores. In fact, I stumbled across a very good vinyl record store. Small, but well stocked. Can't remember the name, but it was definitely on Duluth, near Au Pied du Cochon.
In the same neighborhood (Plateau Mont Royal), we really liked Laloux (
http://www.laloux.com/ )--a very nice French restaurant.
If you like delis, Schwartz's is pretty great. Service with a friendly snarl. Take a seat at the counter for maximum gruffness.
I'm a bit of a bagel aficionado, and I can honestly say that Fairmont Bagel has the best I've tried. (Yes, better than any I've had in New York.)
In terms of stuff to do, strolling around the park on Mont Royal is a great way to spend a couple of hours. (Then you can wander over to Rue Duluth for records and dinner!) We also enjoyed Pointe-a-Calliere, the archeology and history museum. The botanic gardens were pretty good, but what was really memorable was the Insectarium within the gardens. (Better than it sounds.)
The old city is beautiful and excellent to walk around in, but it's very touristy and the restaurants all appear to be major rip offs. I'd do my eating elsewhere.
Have fun!