OK, few trees, no "I shot JR", top five... hmmm...
No trees is hard, though. It sounds like you're looking for mountains rather than "magnificent desolation" such as desert or grasslands or tundra? If so, I'm sort of a "western" guy, so how about:
Glacier National Park, Montana, USA
Wind River Range, Wyoming, USA
Sierra High Route, California, USA
Sawtooth Mountains, Idaho, USA
Weminuche Wilderness, Colorado, USA
I could add places like Grand Teton or Rocky Mountain National Parks, and you could substitute the JMT for the SHR, but that would be my top five.
Depending on where you are in Glacier NP you might encounter Joe Sixpack the daytripper, but there are certainly remote places to avoid him if you try. (I'm researching for a hike there next year at the moment.)
All of these will have SOME trees in lower reaches, though. For true "no trees" you have to head north a bit. So I'm not sure how far you're willing to travel, but I'll add a "Far North" top five as well, taking into account that many spectacular places (ANWR) aren't very accessible:
Banff National Park, Alberta, Canada
Jasper National Park, Alberta, Canada
Denali National Park, Alaska, USA
Wrangell-St.Elias National Park, Alaska, USA
Katmai National Park & Preserve, Alaska, USA
Again, I could keep listing places like Kootenay or Glacier NP of Canada, or bizarre and remote stuff like Auyuittuq or Vuntut or Ivvavik or Gates of the Arctic, but that'd be my top five. You can go on naming ludicrously interesting far-northern Canadian parks all day...