I live in Calgary now and spent over 5 years living in Banff ( also spent a few years in Edmonton, but that's not as consequential).
Now that I have esablished myself as and expert
Let me give you the straight dope. As far as cities go, Calgary is way more interesting that Edmonton is. If it was not for West Edmonton Mall, there would be nothing to see in EDM.
Calgary's city center is amazing. A couple of things not to miss are: Prince's Island Park (close to Eau Claire Market) and the miles and miles of bike/walking paths.
Most importantly: Do not miss Banff, it's only about 90 minites from Calgary and something you have to see. The townsite is very touristy but there are someways to get more into nature if that is your deal. Go north from Banff to Lake Minnewanka, it's about 15 minutes from town and worth the drive. If you have time you can take a boat ride around the lake...but I don't know what it costs or how long it takes.
If you are into hiking, head to the south end of Banff near the world famous Banff Springs Hotel. There are a number of trails that start and end in that area. Also, be sure to take a walk thru the hotel it's quite site to see.
On your drive from Calgary to Lethbridge (or viceversa) you should stop in at my most favourite museum in the whole world: (pause for the name)
"Head-Smashed-In-Buffalo-Jump"
Back in the day our native Albertans if you will, would herd buffalo over cliffs to save themselves the messy task of having to kill them manually. The museum is set right into a cliff-side, so from the exterior all you can see is a door way leading undergound...very impressive.
I could go on more and more if you want. But let me know what sorts of things you like to do and I can suggest more stuff (esp in Banff) that would be up your alley.
Have a good trip, and don't forget to buy a t-shirt.