We're currently on our first trip to Montreal as well and we've had some great meals: Boustan (Lebanese wondrousness), Chez Cora, Eggspectation, Stash (polish cuisine in Vieux Montreal) and we're booked for Europea before we leave. We couldn't get reservations at Toque, though I hear it's more flare than flavor. We'll have to try some of these spots as well.
Since it is your first trip to Montreal, you should try at least one BYOW. It is in our culture now that we bring our best bottle to a great restaurant. When the BYOW started out, it was mostly Greek restaurants but now the restaurants serve excellent food and buy the glasses that go with the appropriate wine. I go regularly to Le zeste de folie on Masson and love that place. It is not traditional French but it has a twist that is interesting. It is not molecular or "foamy", just excellent food! Go on their website and check out their menu...it is worth the detour!
First, there are no street-food vendors in Montreal, so everything will be "sit-down" or take-out if you want to do a bit of pikniking
My shortlist for not too chi-chi restaurants :
Lemeac, Cuisine/Dépendance, L'Express, Madre, M Sur Masson, Justine (Bar à Vin, Terrass & Bistro), Les 3 Petits Bouchons, Confusion/Tapas Du Monde, Bouchonné, BU, Joe Beef, Réservoir, ...
There ya' go.