Driving from Brandon on your way to Calgary, stop into Regina. Tour the Saskatchewan Legislature building then head over to the RCMP Training Centre/Museum. Cruise to Moose Jaw to see the Tudor air planes, Underground Tunnels tours, and have a dip in the Mineral Waters. When you get to Alberta, drop into the Royal Tyrell Museum in Drumheller (amazing dinosaur - fossil museum) and Horseshoe Canyons. While in Calgary, July is the Stampede. Well worth your money... if you like crowds

Heritage Park has a vintage train as well as a village of heritage buildings, Calgary Zoo, Museum of the Regiments (amazing military Museum), Calgary Tower (go have lunch at the Tower in the revolving restaurant... cheaper than dinner), check out Calgary's Crowchild library (jaw dropping library and excellent view of the foothills). Just for fun in Calgary, drive the speed limit on the Deerfoot Trail (listen to car horn honking at ya). Head out to Banff. On the way, stop in to Canmore at the Ice Cream store (I can't remember what it is called now. It used to be the Foothills Creamery). Excellent ice cream. Banff scenary is beautiful. Great opportunity for hiking areas... Johnston's Canyon, Lake Louise. Between Banff and Jasper stop and hike at the Glaciers. Don't forget the sports events in Calgary depending when you travel - football, hockey, lacrosse.
The trip to Jasper and Edmonton is almost a whole other trip. While Edmonton does have the West Edmonton Mall, there is also the sports events..... take in a Edmonton Eskimos football game (late summer - September begins), Edmonton Oilers hockey team, I can't remember if Edmontnon has a Lacrosse team anymore. Edmonton also has the Science Museum and used to have IMax theatre there. In July (or is it August??) Edmonton used to have the Klondike Days (big fair). It isn't called Klondike Days anymore but is neat. Oh! Edmonton also has the Fringe Festival that is really really excellent. Theatres and Music performances. Sometime during the summer, Edmonton also has a Food Festival. Then there is the Royal Alberta Museum in Edmonton. Hope that helps. There is so much to see in each city and town!