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