Hi Sarah,
Here some thoughts on rivers that are within easy reach of Calgary.
Bow River
Oldman River
Red Deer River
Milk River
Based on your experience, I'm assuming you're looking for moving water up to Class 1. All of the rivers above have sections that fit that category. You can find further info on the Red Deer River (and North Saskatchewan River) in Mark's Guide for Central Alberta Paddlers which is available in most Calgary paddling stores including MEC. For info on the Bow River, check this thread:
http://www.myccr.com/SectionForums/viewtopic.php?t=12960. For a 4 day (continuous trip), the Red Deer from Red Deer to Drumheller is a good option. I, and others on the board, have further info on all these rivers, so ask away. All of these rivers will involve shuttles, which is pretty much a fact of life when paddling rivers.
Cheers
Al