Drumheller Royal Tyrell Museum is worth a look if you're willing to take a 1:30 drive North of the city.
Hot springs in Banff + pics at Lake Louise/Lake Moraine. It's still worth going to Banff just to say to people you did. People ask whether you are going to Banff a lot if they find out you're a tourist.
Sky Luge +1. Also hit up the Canada Sports Hall of Fame if that is something you fancy. It's all within the same area as COP.
Eat steak. I had some visitors from BC recently and they were so excited and impressed by a prime rib roast. I'm still confused by that one. But our beef is indeed tasty.
Do you drink whiskey? Try an inexpensive bottle of Alberta Premium if you want to save your wallet a little. It's surprisingly alright. I can't vouch for the Alberta vodka though...
Are you here for the Stampede?
Buy a cowboy hat?
Enjoy no PST shopping? (Not sure how to refer to diff between GST and HST)
Brewery tour? (Wild rose brewery, Minhas...); Minhas you go for the cheap swag, not the brews.
Downtown
- Bow tower (if someone can bring you)
- Devonian gardens (If you're super bored)
- Rundle ruins (if you're more bored)
- City hall and Olympic plaza (Free C-train ride down town)
- Prince's Island park/Eau Claire (How bored would you have to be?)
- 17th ave Red Mile (Side tour after Saddledome?)
EDIT: In case it wasn't obvious...
If it says boring... don't consider it unless you find yourself 30 seconds away from it.
Swap Devonian gardens with butterfly building in Zoo.
Swap Rundle Ruins for Edmonton... actually, still not recommended.
Prince's Island park, swap for Heritage park, or take a look at the bow at vantage points from the Saddledome area.
Night shots? Consider hopping up to Crescent Road or Salisbury Avenue for a nice view of DT. Not as cool during the day, but much more beautiful (IMO) at night.
Amongst the things others have already said and I've repeated.