Two routes which can be stitched together to make a lazy two or more day traverse are FS 300 out of Lander to South Pass and BLM 2302 from outside of Atlantic City to US 287 near Sweetwater Junction. I believe the former is locally known as The Loop and the latter is the Atlantic City-Hastings Road.
The Loop runs through the Wind River Range for about 35 miles from the end of WY-131 near the Sinks State Park to WY-28 at South Pass. It reaches about 9,500' elevation at Blue Ridge and holds high elevation most of the way. Its heavily forested, goes by two alpine lakes, passes over the Little Popo Agie River on a high boggy plateau, and sports a number of traiheads. There are NF campgrounds at each of the lakes and I assume disburse camping is allowed much if not all of the way through. The larger of the lakes is Louis Lake and is closer of the two to WY-28 and FS-300 is good enough from there to the lake to allow passage of trailers including larger RVs. From the Sinks SP to Louis Lake FS-300 narrows down to good two-track and is steep in places.
From just east of Atlantic City (population 57), BLM Road 2302 runs about 30 miles over the large, treeless foothills of the Winds parallel to the Sweetwater River and the Oregon Trail and Mormon Trail. A ridge-runner, 50 to 100 mile views can be had in many places. There is a stark unshaded BLM campround towards the eastern end and some short spurs descend to creeks and springs with a few cottonwoods. In the summer months, groups of LDS (Mormon) re-enactors use 2302 to reach memorial sites where dozens of "handcart company" emigrants died in an early winter blizzard in 1856. About the first 10 miles off of the good graded road leaving Atlantic City are two-track and ungraded and should be considered impassable when wet.
Foy