I presume you're only staying one day in each place, which is pretty tight. Anyways, I'll try and help you maximize that time. In Quebec City, just stick to the old town.
The beautiful Chateau Frontenac, the historic Planes of Abraham and the old fort at the top. Really, this is the only place you need to be and you can easily fill a day of it. In Montreal, you have a lot of things to do.
You can go to the old town (vieux Montreal) which is right by the river. There is the gorgeous Notre Dame de Montreal church, which is worth a look. So is Mont Royal (Mount Royal) and the Oratoire Saint-Joseph on there.
There also is the Olympic Stadium with the fun funicular that you can take to the observation tower. Right beside it is the biodome, which is unique. Regardless of what you do, make sure you head to Boulevard Saint-Laurent for lunch or dinner, as you have an endless choice of restaurants.
Ottawa is a government town with mostly historic sites. At the moment there is the tulip festival going on, which is nice. You can also get a free tour of the Parliament buildings, which is highly recommended.
There are other museums you must pay for. The Royal Canadian Mint, where they manufacture coins, is quite interesting. The Canadian War Museum is unparalleled and excellent for anyone interested in history.
You also have the option of going off to see the RCMP stables where they keep their infamous black horses and train for their performances. For a hotel in Montreal, take a look at the Travelodge downtown. It's not the best hotel in the world, but the price is great (just found it for under $70 CDN/night on Travelocity.ca) and the location is excellent.
Have a great trip!
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