I live in Montreal, so if can recommend a bunch of things.
There's a million things to do here. Check out the standard tourist things -- the Old Port, Notre Dame, St. Joseph's Oratory. Do some shopping on St. Laurent, have a coffee in an outdoor cafe on St. Denis, visit a pub on Crescent, go to a night club on St. Laurent....
One of my personal favourite things is the food. If you're interested in seeing one of the best outdoor markets in the country, visit Marche Jean Talon in Little Italy. Incredibly good, quality food (and much cheaper than the more famous Atwater Market) with lots of free samples of the produce everywhere. Buy some nice cheeses, wines, deli meats to take home with you -- and if you feel like eating some of the cheese right away, grab a baguette at the Patisserie Moisson at the market for some of the best bread in the city (they also have amazing pasteries, I highly recommend trying one).
There's also a lot of great restaurants. Some of the classic ones are Schwartz's for a smoked meat sandwich, pickle and cherry coke. Also Fairmount or St. Viateur for the famous Montreal bagel. St. Viateur has some great cafes, where they serve bagel-sandwiches. A lot of people want French food when they visit Montreal, and if you're in that boat and want to try the classic Bistro style French food, I'd recommend L'Express. If you're looking for a specific cuisine let me know because just about every ethnic cuisine there is can be found in Montreal.
There's also some great micro-breweries in Montreal, if you like that sort of thing. One of my favourites is Dieu du Ciel (God of the Sky) on Laurier and St. Laurent. There's also Cheval Blanc (White Horse) which is quite popular and Le Mer a Boire (The Sea to Drink).
The tam-tams is quite interesting as well if you're planning on seeing Mont Royal. Every Sunday hundreds of drummers gather at the base of it by Parc street and you can hear them about a kilometer away. If you go prepare to get high from the fumes

It's quite a sight to see (and hear).
There's a festival of some sort every week in the summer in Montreal. Its the Blues festival (nowhere near as big as the jazz festival though) during the dates that you're here, if that interests you the website is here:
http://www.festiblues.com/
Anyway, as you can tell, I can go on and on about Montreal, so I'll just stop now

Let me know if you have specific questions.