The majority of the mountains around Rossland(red) and nelson offer little alpine. Treeline is around 6500ft and most of the peaks are in the 7k range. Things change considerably as you go a little further North.
The interior is a funny place. The roads follow valley bottom, and there are too many mountains, to even see the real mountains. You'll catch a glimpse of one here of there, but for the most part you will be in the "foothills". There are tons of forestry roads that can get you to the goods, but you will need a sled or a very strong will to get there. From the car touring options, look at Kootenay Pass. or Rogers. Of course there are options from the resorts as well.
Huts are the way to go, and the best way to ski BC. The Alpine club of Canada huts are cheap, although they are rustic. Bring your own sleeping bag etc.
If it were my trip,
1. Red Mountain
3. Jumbo Pass Cabin
5. Rogers pass - Asulkan or Wheeler hut.
Then come back down the same way. (or head back through golden and fernie)
The Jumbo Cabin will require a flight in, has huge mountains(the biggest), but the hut is on the ridge and I would imagine most of the skiing done is short shots around the cabin(1-2k vert). Although there are 4-5k lines in every direction. The Jumbo snowpack is more continental, fairly similar to UT. Jumbo will give you isolation, but a lot of it has been logged, hardly pristine wilderness. Which spoils the view, but offers fun skiing. The cabin is usually available.
The Asulkan hut at rogers, is popular. Has big lines, and glaciers at your doorstep. The snow is stickier than jumbo, and steep lines will be more filled in and the pillows that form on everything will be a refreshing change of pace. Plus the glacier skiing is at your door step Rogers is popular and accesible by car, so you will see other people. There is no logging.