I'm not sure if there's a "better" route but I've been going up to Jackson for the past 30 years from So. Ca., and have always gone up the 89 beginning in Brigham City, off the I-15, north of SLC. It winds through Logan Canyon following the Logan River and then down into Bear Lake just before you hit Idaho. There are campgrounds around the lake including a KOA in the town of Garden City but the one we stay at is the Rendezvous Beach state campground at the south end of the lake. After leaving the Bear Lake area it winds through farmlands and some small towns into Wyoming and then through the Star Valley. Beautiful drive with good roads and little traffic. It's about 3 hours from Bear Lake to Jackson. We do it in a 30' class A.