I live in Calgary.
For the Stampede rodeo, see if you can get seats in the infield or even better in the Lazy S saloon or Ranahans if you have some serious $$ or the upper levels in the shade and out of the rain if it does. Being in the sun all day can be tough, especially if having a few drinks. As mentioned above, Banff and Jasper are beautiful, Morraine lake is where you want to try fishing if possible( outside Jasper). You cant go wrong with hiring a guide on Lake Minnewanka either, just adjacent to Banff as well for Lake Trout and big Lake whitefish. Always a few wild critters on the side of the road or in either town site in the park. Calgary sure is expensive for rooms at that time but so is everywhere when its the best time to be there. I'm sure you will love the exchange rate for your US dollars and that balances things out a lot.
Whatever you do, don't make your way back to Calgary on a Sunday afternoon from Banff as the highways have been so busy the past few years during the summer its a crawl for about 50 kms as you get close. The last 50 KMS can take an hour or more if coming back from the mountains and getting caught in the choke point of traffic.
For those ten days every summer, almost everyone puts on their western wear and plays the part.
Greatest Outdoor show on Earth is what they call it!