WY Hiway 14

14 is a typical Rocky Mountain Road. There is a significant climb, but the grades are not too steep. Not a great deal of shoulder room in spots. There are some great dry camping spots along the way, and one Forest Service campground with electricity (Sibley Lake). There is a dump station at Burgess Junction. The descent into Ranchester is similar to the climb to the top, Somewhat long, somewhat steep, but doable if you have some mountain driving experience. Look for Moose along the way, they are common to the area.
14A is way too steep in spots, do not take it.
Another alternative is 16. That climb is not quite as steep or switchbacked as 14. Also very scenic. That route is Greybull to Worland, thru Ten Sleep and up and over into Buffalo.
Finally, should the mountains make your knees shake, you can go from Greybull to Laurel Montana and then pick up Interstate 90 and never have a mountain to climb. It would add around 120 miles to your trip, but probably less than a hour to the drive. It really isn't a bad option for those who fear the climbs, the dropoffs from the shoulder, people who don't like the fact that their rig might only be able to muster 10 MPH while climbing, and those who will melt their brakes while riding them during the descent instead of shifting into a lower gear.