How much time you got? (It will take ~ 26 hrs driving).
Fast is I-84 to 80. Stay in Ogden UT Area and, Vedawoo, WY (between Laramie and Cheyenne BEST star gazing in Aug) IMPOSSIBLE In winter (any month EXCEPT Aug in WY). Nice break at Sidney, NE Cabela store and RV park (free)
For more time / fun / scenery, take I 90 and enjoy MT, WY(Sheridan, Chimney Rock), SD (Black Hills)... ~ 30 hrs
for
Semi BEST trip...I- 90 > Livingston, drop into Yellowstone, loop to Tetons, back out NE Yellowstone (Beartooth Hwy (most scenic in USA...), then over the Big Horns (14a and 14 into Dayton / Sheridan), on to Chimney Rock (after seeing indian war battlefields near Sheridan / Buffalo / Story, WY). enjoy trips trhough Black Hills and Custer State park (Needles Highway) then on to Wall Drug and Badlands., Cut south to Chardon, NE to catch
http://www.carhenge.com/ on south to Sidney, NE or SE to Paxton for
Olies BIG GAME bar (if you can handle it...)
http://olesbiggame.com/
I like
Pioneer Village in Minden, NE (would be a GREAT NE history lesson + you can see a dog powered Clothes Washing Machine (good idea, and the DOGS love it (excercise))
WHERE’S THE DOG? ITS WASH DAY!! - True West Historical Society
Nearby Windmill State Park is GREAT.
Use some other planning tools...America's Byways®: National Scenic Byways Online
The Enchanted Highway Virtual Tour - Regent, North Dakota
Ca
mping resources:Free Campgrounds for RVs
Free Campgrounds in the USA
Most small towns in WY offer free camping at city park (POWELL IS BEST). Fairgrounds too!