I Heart Montreal
Montreal is an incredible city, and I don't just say that because I'm from here! As for hotel's, I'm not really sure what to suggest because I haven't stayed in many myself
If you're looking for a large, upscale place downtown try the omni, it's one of the few with an outdoor pool and it's pretty much at the city center (located on Sherbrooke Street) or you could always play it safe with the Sheraton on St-Jacques, very nice too. Of course boutique hotel's abound here, and Hotel St-Paul or St-James in Old Montreal I've heard plenty of good things about.
As for shops to visit, I'd love to suggest Terrafolia but we're outside of the city, so it would require a car rental. PM me and I can direct you if you're interested, would be great to meet fellow FCers! Otherwise, you should maybe pay a visit to The Flower Pot located on Notre-Dame, not too far from Old Mtl... close to the Atwater Market (another of the city's gems).
Places to see... well I would suggest St-Joseph's Oratory, tons of Churches are scattered all over the city, but St-Joseph's it likely the most famous. Don't forget to check out what festivals are happening while you're here... ie. Just For Laugh's and the infamous Montreal Jazz Fest are always hits.
Don't forget to try Poutine!! (my personal fav at the Orange Julep on Decarie) and REAL Montreal Smoked Meat (from Schwartz on St-Laurent)
Hope that helps with your visits to La Belle Province!