Well, if all of the US is in play, except Yellowstone, given your timing I'd still be thinking the mountain west. Idaho/Montana/Wyoming/Colorado. Just a HUGE area. Your one trip to Yellowstone is only touching a small portion of it. And in the west, late July/early August is getting close to prime time, as August and September are considered the peak of their season. In April-early July when we are peaking in the east, they have too much runoff in the west, and things don't start settling down till later in July or into August.
The Bozeman area of Montana and Henry's Fork region of Idaho are in "greater" Yellowstone, so if you intend to hit up those areas on your later trip, well, then disregard them. If your later trip will be more within Yellowstone itself, then they are options.
But farther off:
Missoula area - The Bob Marshall Wilderness, or Bitterroot area. I have no experience in this area, but have heard lots and lots of good things.
Central Idaho - upper Snake River area. The center of the Frank Church Wilderness is massive and inaccessible without guides and rafts. However, the route 75 and 21 area between Lowman, through Stanley and Sunbeam, and into Challis is accessible. Low population, but has the basics. Some lodging and/or campgrounds throughout. There's a great diversity of water, from moderately large forks of the Salmon to small mountain streams. From flatland meadow, limestoners, to fast mountain water, just crisscrossing the whole area, not to mention the high lakes. There are dirt roads reaching into the wilderness areas. I spent a little time in this area when I was just a novice and loved it, and wish I could get back there. I think I could spend a few years in there and still not be satisfied that I'd covered it all.
Colorado - covered by others.
