Theodore Roosevelt NP?
EDIT- Actually, I just looked at some pics from TRNP, and I guess not.
Do you want NO trees, or would savannah be OK? Like the Serengetti?
Baffin Island? (Actually, anywhere in the far north of Canada.)
Kayak South Georgia Island, or the Aleutians, or Little Diomede. If that doesn't make you feel small and vulnerable, nothing will.
Death Valley? Surrounded by mountains, though- it might not feel so large as you are describing.
There are a few National Grasslands here in the U.S., but they aren't huge. Maybe they'd do for a quick fix but they aren't really "lifetime goal" material.
There are parts of the Australian outback that may as well be on a moon of Jupiter. Several folks here can tell you about it.
Mongolia. I've heard several glowing trip reports from the region.
The more I think about it ANWR and that region of Alaska sound like what you're looking for. I have often daydreamed of a 20-day float down the Colville River. It's one thing on my life list that I'll probably never do...
An even better alternative might be the MacKenzie River in Canada. That's an epic!