Monty, I spent some time in Calgary last year. Don't even try driving to the rodeo. The traffic is horrendous, and you will have difficulty finding a place to park. I parked the Airstream here.... Calgary West Campground - Enjoy Our Famous Western Hospitality!
The best part about the Calgary West Campground is their shuttle to downtown Calgary which is not far from Stampede Park. They also accept dogs. Despite being on the outskirts of the city, I found it to be fairly quiet. They are also right beside Olympic Park (site of the 1988 Winter Olympics). You can go right to the top of the ski jump tower; it offers a breathtaking view of the Rocky Mountains. Be sure to book early. Accomodation/campgrounds during Stampede Week sell out quickly.