What do you like to do? January could be bitterly cold and you'll probably want to stay indoors (NMC and aerospace museum are good choices) or a Chinook could roll in and bring warm weather for the day. If there is nice weather I would suggest visiting the NMC and then wandering down towards the river and walk along the pedestrian paths which leads you into downtown. Make your way to Stephen Avenue which is a pedestrian street and it has plenty of restaurant choices. The Calgary tower offers a nice view of the city although the price is $18.00 to enter. There's also the Glenbow Museum if you are interested in local history.

Since you have an early flight I'd suggest staying at or near the airport and taking transit (there's a direct bus available) to downtown for the day if you don't want to rent a car.

FYI: the Aerospace Museum's location isn't really transit-friendly but it's about a 10-15 minute drive from the airport.