The List Could Be Endless
My apologies for taking so long to get back to you. I'm a big fan of both the lesser-known units of our national park system and our 50 various state park systems. So let's see which of those might suit you.
Between Salida and Montrose CO, yes, you'll be going by the Black Canyon of the Gunnison, but you'll also be passing Curecanti National Recreation Area. And on your way into Arches National Park, you might want to hike some of the Fisher Towers Trail.
While in SLC, check out Antelope Island State Park. Although the island is 'off shore' there is a causeway out to it. There is also a $10 entrance fee, but in the grand scheme of things for this trip, that's an incidental expense.
Unfortunately, I've taken too long to respond to your post and so your map has disappeared from the web. So from SLC northwest, I'm working just off your description above....
Between SLC and Jackson, although it involves a bit of backtracking, I'd suggest that rather than using I-15 north for a significant portion of that drive, you head east and north from Ogden on UT-39/UT-16/uT-30/US-89 around Bear Lake to Jackson. Those are all scenic roads and they will take you by Bear Lake State Park UT and Bear Lake State Park ID.
While in Billings, note that Little Bighorn Battlefield is just about 50 miles east of there. And while I don't have a lot of suggestions for things between Billings and Glacier, those are all scenic roads and you might want to check out the Museum of the Plains Indian.
Between Glacier and Missoula, I'd probably use US-93 down the west side of Flathead Lake with potential stops at West Shore State Park, then Big Arm Unit of Flathead Lake State Park, or National Bison Range.
AZBuck
Feel Free to Disagree, But...
"Is 39 worth the extra time?" That's up to you. I would definitely trade 2 hours of driving through a built-up area (SLC/Ogden/Brigham City/Logan), all on superslabs of four-lanes, for a 3½ hour drive on two-lane scenic byways over the Wasatch Range. You may also want to take into account two other factors: There will be minimal, if any, services along UT-39/UT-16/UT-30 aside from the small towns of Woodruff and Randolph; and the speed limit along most of that route is 55.
"[W]ould it be worth skipping Soda Springs and Idaho Falls and going straight to Jackson from Montpelier via 89?" Again, this is a matter of taste as much as anything else. As noted above, I will almost always choose byways over Interstates, especially when the byway does not go through any large towns and the Interstate does.
AZBuck
