I live in Montreal, and this is my advice:
1. Get hotel anywhere in the downtown core. (Ex: Comfort Suites, Holiday Inn, Mariott, Omni or Sofitel if you have the money... or check out ONESPOUT.COM for Montreal daily deals, they often have deals on hotels and such.)
2. Clubs: If you're 20, you'll like the street Crescent & St.Laurent. All of Crescent, and St.Laurent between Sherbrooke and rue Prince Arthur is fun. Even a little more above Prince Arthur...
3. Definitely check out the Portuguese Area (as mentioned below), it's where many of us Montrealers hang out. This is near street St.Denis/Sherbrooke. (or metro: Berri Uquam)
4. The old city (or as we call it, Vieux Port, Old Port...) is gorgeous in the spring/summer. Go in May the earliest, before that, it's not very happening. Maybe plan a day at the Scandanavian Spa, or spa BOTA BOTA. (Spa on a boat, gorgeous views of the city. And you can do the 'hot/cold' baths for only 50$ each.). I wouldn't eat in the old port though, (very touristy), but I would recommend 'Jardins Nelson', or restaurant 'Holder'. Keep in mind there are a lot of BYOW restaurants too (if you're on a budget), there's STEAK FRITES, L' Academie, (some of the few better known, and easy to get to...)
5. There's the museum of Fine Art in Montreal which is gorgeous. And many other's. Everything is walkable (depending on the weather) or 100% reached by the underground metro. Which IS safe and EASY. 3$ a ride.
6. If you go to Quebec City, (maybe after seeing montreal?) Take a train or BUS (big bus terminal near Berri Uquam metro...). Quebec City is very touristy, so you won't have a problem getting around, or speaking english. Just do your research first on where to go to eat, my friends have had problems with that (expensive and touristy, not good food. And there are many nice restaurants in Quebec City, so do the research!:) .)
Have fun planning your trip!