Having a quick look through my photos from 2000, look at these places. You can plot a circular-ish route out of Vancouver and back. There aren't many roads to choose from.
Athabasca Glacier, Icefield Parkway. North east of Vancouver, maybe 300 miles or so. Take a Snow Coach on to the ice and walk around. There's a hotel across the road from the glacier (Columbia Icefield Chalet), which, if you plan on staying, you will need to book well in advance. Some rooms have glacier views.
Athabasca Falls. Not far from the glacier.
Hellsgate Airtram. Descend in to a gorge via cable car.
Brandywine Falls. Can't remember exactly where, but a very nice waterfall. Somewhere between Vancouver and Athabasca.
Emerald Lake. Peyto Lake. Lake Louise and its Natural bridge. All very picturesque.
Sunwapta Falls.
People rate Jasper and Banff. I didn't. Jasper has a cable car with nice views. I can't remember anything significant about Banff apart from it being touristy. It's ok I suppose.
If anybody mentions the Inside Passage trip - car ferry from Prince Rupert down the coast to Vancouver Island....... maybe an hour of interest (max) looking at the forest-lined coast. Then 12 hours of boredom looking at the same scenery again.
You should be able to find all these places with a bit of google and by looking at a map see a route that takes you as far east as the Athabasca area and as far north as Prince George before turning south back down to Vancouver.
If you can, take your car on the ferry across to Vancouver island and spend a bit of time there.
In the unlikely event that you find yourself with days to spare then you could try crossing the border in to Seattle, which is a reasonable place to visit. If you think it may be a possibility, note that you must apply for the electronic travel authority online at least 3 days before entry in to the US, so do it well in advance and it's valid for 2 years.
