Here's a great ride for a weekend, suitable for even the complete novice. It's a ride to Chestermere and back on the irrigation canal pathways. You don't have to ride on the roads at all, unless you want to make a lap around the lake once you get there (and those are quiet, wide residential roads with 40 km/h speed limits). As a bonus, there are NO hills, and the only difficulty might be a bit of wind once you get out on the prairie.
I started my ride at the Ship & Anchor after meeting with another BikeCalgary director for lunch, but you could start anywhere along the Bow River pathway system, or even drive to somewhere like the Inglewood Golf Course or the Fish Hatchery, park there, and ride on. My total distance was 71 km and I spent 3.5 hours on the route, including a few short stops. If you're not in a rush, you'll want to book an entire afternoon for this outing.
You'll want to ensure you've got a good maintenance kit with you including a pump and tire patches or spare inner tube, because you'll be a long way from assistance at some points along the route. My rear tire got a little low en-route, and while I had a pump it wasn't very good, so I was happy to meet another road-bike rider with a better pump than mine.
The complete route, along with several pictures, is posted on my Nokia Sportstracker page.