I live in Canada, actually not far from the Rockies 
Hubby and I honeymooned in Jasper.
Where you should go depends on what you want.
If it's big city and exciting events you want, you may like to go down east. Toronto and Ottawa are beautiful. Ottawa is the national capital and houses the Canadian Parliament buildings. Toronto is Canada's largest city.
In the west, Calgary is a nice place to stop. You're only an hour from the mountains (Banff) and only an hour from the badlands (Drumheller; effectively the Badlands is a desert and there have been some important fossils discovered there - Drumheller hosts the Royal Tyrrell Museum of Paleontology and the whole town is dinosaur-themed). Calgary has some really neat attractions, including the Calgary Zoo and Heritage Park. The latter is a "living history" museum detailing the early days of the city. You'll get to see replicas of how life was lived in earlier times and there are costumed docents who are in character.
If you rent a car you can drive up Highway 93 from Banff to Jasper. This takes you right through two national parks and it's very scenic. You can stop on the way at the Columbia Ice Fields and see a real glacier - even in the summer! Jasper is much less commercialized than Banff. There is actually a commercial development ban in Jasper. You can't develop on virgin land anymore. Just as an FYI - wildlife roams freely in the parks. As in, you might spot a deer on someone's front lawn. Make sure you stay at least 3 bus lengths away from wildlife and double that from bears. If you're going hiking, make plenty of noise to ward off wildlife. Attacks are rare, but you can use common sense to help prevent them. (You would be amazed at how many tourists act as if the wildlife is completely tame. All of them are WILD.) If you do see a bear, make sure you report it to a ranger. It's not a problem, usually, but they do keep track of bear activity and will humanely capture and rehome problem bears. The mountains can also be cold year-round, especially at night, so dress warmly.
In southern Alberta, where I grew up, you can go to see Waterton-Glacier International Peace Park, which crosses the Canada-U.S. border, and Writing-On-Stone Provincial Park. Waterton is very close to the Crowsnest Pass, a string of small communities nestled right in the Rockies. The Pass features a museum of local history, Frank Slide (the site of a massive rockslide that partially buried the town of Frank), and the Bellevue Mine, a real coal mine that you can tour. A little east of the Pass is Fort MacLeod, the site of a historic RCMP fort. Just beyond Fort MacLeod is Head-Smashed-In Buffalo Jump. This is a UNESCO World Heritage Site and was used by Canada's indigenous peoples for centuries to hunt buffalo.
A word of advice about visiting national parks - staying there can be VERY expensive. You have to purchase a pass to even get into the park, and display it on your windscreen. When Hubby and I go to national parks, we usually either camp in a provincial park nearby, or stay in a nearby community. Usually we camp at Police Outpost Park when we visit Waterton, and stay in Hinton when we visit Jasper. This cuts down on cost.
I haven't actually been to Vancouver but have family there. It's a really neat place - you can go see Stanley Park, which features centuries-old trees, and you can check out some local artisans and hipsters.
Keep in mind that Canada is a HUGE country. You can't do all this in one trip. It takes us 9 hours to fly from Calgary to London. Alberta alone (the province where we live) is 20% larger than France. You'll want to decide what you'd like to see and then book your flights accordingly.