I think BYU would be fun in a Mormon kinda way. Would probably add a stop in Moab in there too
I drove through BYU, Utah and Utah St campus/stadiums on my last trip up to Grand Teton National Park.
If anybody remotely enjoys outdoor life it's top road trip in new Big 12. There are obviously great places to hike, camp, climb and backpack all over Utah, but you don't even have to go far from BYU campus to be in some very beautiful areas. There were what looked like 1000s of college kids tubing down beautiful mountain river almost right next to campus.
It's actually not a bad drive up to Yellowstone/Grand Teton. Probably similar distance as the Utah national parks. In early fall I'd prefer Yellowstone/Teton. In later fall I'd prefer Zion/Bryce Canyon/Moab areas.
BYU campus itself isn't any different than any other and the stadium seems appropriately Big 12 big time.
Utah stadium same way, but campus and stadium are more in the middle of town where BYU seemed closer to mountains. Utah St town and campus and stadium were nicer than I'd have guessed too.