Three weeks is ample time to do a circle tour that would include the Alaska Highway in British Columbia's north. This would include a quick dip into Yukon too, near Watson Lake.
The Cassiar Highway on the northwestern side of B.C. is one of the best routes for seeing bears and glaciers.
The Alaska Highway between Watson Lake and Fort Nelson is where the caribou, bison and bears hang out in late August or early September. As well, Liard Hot Springs provincial park is a great spot to spend a couple of nights soaking in the pool and relaxing.
The Cassiar and Alaska Highways have terrific provincial campgrounds. The Cassiar has three by lakes (Meziadin, Kinaskan and Boya) and the Alaska Highway has Liard Hot Springs and historical Kiskatinaw, as well as two campgrounds lakeside at Muncho Lake and another lovely one at Summit Lake. Watson Lake also has a gov't campground that is very nice BUT we usually opt for the commercial campground here to clean up and stock up at the nearby grocery store.
The Okanagan can easily be included northbound or southbound, via Hwy 97.
Having said all that, I must admit to also greatly enjoying the Kootenays in southeastern B.C. Very scenic. Relaxed. Good campgrounds. Soothing hot springs.