I'm not very familiar with northwestern Utah only because I never seem to be able to tear myself away from southwesternern Utah once I'm there.
But I've been to Bryce, Zion et al in summertime and found them nearly empty due to the heat. Capitol Reef and some of the higher elevation parks were probably more crowded. One June I spent 4 days in Moab and only saw 2 other bikes.
Your mileage may vary.
In southwestern Utah there's the Burr Trail, which is couple hundred miles long and intersects main roads in a few locations. The Paiute ATV trail. The Silver Reef area is right off of Interstate 15. We poked around there in a small car but want to go back with our TW's. I think you can sneak into Zion from there. Lots to do. Wish I had more info further north.