Well, you could get up on the first day and head down to the OEB for breakfast. Once that is done, head down one of the rental places in town, pick up a raft and take a float down the bow for the entire afternoon. In the evening, head down to the National on 10th for something to eat and try your hand at some bowling.
On day 2 you'll probably be hungover like hell and you'll be getting up pretty late in the afternoon. Peel yourself out of bed, and load up on bacon at diner deluxe. Once you've fed yourself, wander down the hill into downtown and enjoy some of the cool sights down there (peace bridge, the giant head, other street art). See if you can find a bored Cenovus or Encana employee to take you up to the 56th floor of the Bow. If you're less interested in making friends with random oil company employees, buy a ticket and get up the Calgary Tower. Once you're done looking at the mountains and standing on the glass floor, get back down to street level, cross 9th and get your eat on a Charcut. There's a plethora of bars, live music and all sorts of **** to entertain you downtown for the rest of the night. Might I suggest some late night authentic Asian Karaoke at Nanta? Comes complete with giant beers, rowdy locals and a staff that's way too tolerant of their guests.
Day 3, lets work some of that booze out of your system from the last couple days of going crazy. Take a quick drive over to Nose Hill and walk amongst the wild grass lands that Calgary used to be before the crazy urban sprawl swallowed everything up. If walking hills isn't your thing, go down to fish creek, or the trout hatchery (they're in very different sides of the city, so it'll probably be one or the other) and enjoy some of the other actually nice parks in town. Later, after lunch at one of our world class eateries, go to Winsport (Calgary Olympic Park), where you can take a ride down the bobsled track or zipline off the highest ski jump tower. While you're there, remember to pop into Canada's Sport Hall of Fame and get lost in some of the greatest Canadian sport memories. You'll be across the parking lot from Hockey Canada's headquarters there as well, so if you're feeling super adventurous, sneak up to the 2nd floor and introduce yourself to Tom Renney. I'm sure he won't mind. Hit up Notable in Montgomery for something to eat when you're done at Winsport. It's a couple blocks off highway 1 and totally worth it.
Maybe on Day 4 you'll be ready to leave the city but already done the mountains/k-country thing, might I suggest a quick drive out to the badlands and visit the Royal Tyrrell Museum? It's nothing special, just the world's premier Palaeontology Museum. Don't leave without finding the 1 m in diameter Ammonite covered in gem quality Ammolite. One of my favourite things in a place full of the coolest fossils in the world. When you're done there, drive 2 minutes down the road and play 18 holes at the Drumheller G&CC. A great little course with a back nine to die for (watch out for snakes if you hit it into the scrub).
Unmentioned: Waterton Lakes National Park, hiking in K-country (Highwood Pass FTW), Frank Slide, the Okotok outside of Okotoks, taking a brewery tour at Village Brewery, golfing in Canmore, hitting up a local small town rodeo, not dying in a kayak in Harvey Passage, fishing the Bow River in downtown Calgary, the Ironwood in Inglewood, watching the Dawgs at Seaman Stadium, Telus Spark.
