Others have some good suggestions here like Kokanee provincial park near Nelson. You could also camp somewhere north of Kaslo like Lost Ledges campground (Provincial campground right on Kootenay lake) and then drive to a number of hikes such as Monica meadows or Kokanee park from the East side. Another suggestion would be to camp in one of the forestry sites along the Horsethief creek road west of Radium and then do one of the many hikes up that drainage. Lake of the Hanging glaciers is a beauty and there are many others in the trail guides. The idea of Whiteswan lake and then day hikes in the Top of the World park is a good one though the 1 hour drive then a 1-2 hour hike to the start of the day hikes would make your days fairly long unless you pack a tent in and camp at Fish Lake. The hike to Fish lake is an easy one on an excellent trail and there are 4 really nice day hikes from the lake.
You and others are correct in concluding that the roads and campgrounds are all at low elevation so you are faced either with a long hike to the alpine or a drive up roads which often are rough followed by a pretty long hike.
Let me know if you need more advice re: the East Kootenays as I hike a lot around here.
