Its one of the finer cities out there in my biased opinion.
Stampede week - 10 day party of general debauchery, a great experience but if big crowds of non-cowboys/girls acting like some while severely intoxicated doesn’t sound like your jam I wouldn’t plan too much time around it. Also tons of live country music to take in.
Flames games - Look I’m going to be honest with you, the Saddledome is a bit of a dump if you been to any of the newer arenas around the league, but its still a great time on a friday/saturday night especially if were playing a Canadian team. Hit up Stephen Ave or 17th Ave for pre/post game drinks/food
Food - I think the food scene in Calgary has really taken off in the last few years, tons of great restaurants with a variety of different foods. In terms of price to quality (especially give CAD/USD ex) I would argue its some of the best value you’ll find in major North American cities
Craft Beer - A number of great craft breweries have opened up in recent years, a lot of them are located fairly close together so its a great way to spend an afternoon touring around them (https://www.barleybeltyyc.com/). Also seen a bunch of distilleries pop up recently and have a number of good cocktail bars if thats more your style
Music - Definitely not in the caliber of some of the great music cities in the states, but there are a lot of pretty good music venues in the city from dive bars to orchestras. Several music festivals throughout the summer as well
I know you said non-tourist ideas only, but you’re doing yourself a disservice if you come up here and don’t get out to the mountains in some form. Banff/Lake Louise are the classic stops but also tons of hikes in the Canmore & Kananaskis areas. Also lots of pathways and parks in the city to take advantage of.
And because @cav007 couldn’t resist taking a shot at Calgary I feel necessary to mention that Edmonton’s not hell, but you can see it from there