What fun! I have spent lots of time in all three cities (and lived in Ottawa for many years), and what I love about all of them are the festivals. I am not sure when you are planning on visiting (late August?) but check out the tourism sites and find out about festivals going on when you are there…I think the Montreal Blues festival is on in August at around that time.
Also, for all three cities, you can usually request free maps and tourist guides online (makes life easier!).
Quebec: Visit the old part of the city, but be aware that there will be many many tourists around the gift shops. If you are staying in or around the old part of the city you can pretty much walk around on your own without too much hassle. You can wander through the old city and learn lots about the history of Canada: for instance the old fortifications and the Plains of Abraham (where the French battled the English), and also take the funicular for a view down to the water. For places to eat, I would just wander around and look for a small non-chain restaurant (sorry, no specific recommendation) or go to a market and buy fresh bread, local cheese and some other deli items and have a picnic.
Montreal: More to do in Montreal because it is bigger than Quebec! I second Schwartz’s, although I admit that last time I went I only ordered the fries because they are SO good). St-Viateur Bagels are supposedly the best, athough as long as they are real (dipped in honey water and cooked in a wood burning oven) a Montreal bagel is probably one of my favourite foods. Montreal also has some great restaurants: Olive & Gourmando for lunch (http://www.oliveetgourmando.com/index_flash.cfm), Garcon for pricier french food (http://www.restaurantgarcon.com/), and Au Pied de Cochon (http://www.restaurantaupieddecochon.ca/) for some mid-range food. Montreal is also a popular shopping destination (clothing, shoes, interior dec, etc.) for those that live in more style-conservative areas of the country and feel deprived. If it is a nice day, the botanical gardens, a walk up Mont Royal (the big hill/mountain in the middle of the city), or a walk in one of the numerous neighbourhoods would be nice (Westmount is a well off english neighbourhood if you are craving some English). Montreal has great public transit, so you can ditch the car and take the Metro most places.
While in Quebec (the Province, not the city) enjoy being able to purchase (some limted) alcohol in the corner stores. All the other booze will be located in an SAQ (liqour control store) – important if you want to pick up a nice bottle of wine!
Ottawa: As the Nation’s capital, you should try to visit the parliament buildings (they have regularly scheduled tours in the summer), perhaps see an RCMP changing of the guard in the morning (the Royal Canadian Mounted Police have guards in dress uniforms wearing large bearskin hats who perform a changing of the guard ) on parliament hill, wander a few blocks to the Byward Market which is full of bars and restaurants and some little boutiques. Ottawa is a government town and doesn’t have as much of a nightlife as Montreal, however it is concentrated in the market which is nice! No specific restaurant suggestions in Ottawa since I tend to prefer dining at my grandmother’s when I am in town! Ottawa is also museum and gallery central (http://www.ottawakiosk.com/museum3.html). Definately check out the National Gallery (big glass building, hard to miss) and the Museum of Civilization right accross the river in Gatineau, Quebec. Also just accross the river is Gatineau Park with lots of hiking, some old historic houses to visit, and swimming in lakes. Finally, the Nation’s capital is home to the National Arts Centre where you can go to watch a ballet, take in some classical music or watch an opera.
Handy tip: all alcohol is sold through LCBO (Liqour Control Board of Ontario), but you can find them relatively easily (there is a large one within walking distance from the market). I know this may sound like I am an overly dedicated LCBO client, but these things are important!
OK that was long! Are you driving, taking the train or flying?