Most definitely visit Old Montreal. It's beautiful, and there's lots to do.
There's so many things to see and do in Montreal. They've got a cool planetarium. I'd check online to see if any festivals will be going on while you're there.
The nightlife is great, as is the shopping and food. Spend time on Ste. Catherine Street. There's always lots going on there. Try Montreal bagels, smoked meat and poutine (don't get that from a fast food chain, get it from a real Montreal place). Go to Dunne's for their great cheesecake.
There's lots of nice architecture, ie Notre Dame. Mont Royal is a nice site to walk around.
If you like amusement parks, there's always La Ronde.
They've got a good symphony and plenty of theatre, too. You might want to check Place des Arts to see if they've got anything good playing.