A lot depends on if you want scenic, or if you want easy driving through vast areas of somewhat flat nothingness. For scenic I would suggest the route up to Saratoga WY spend night there, and maybe soak in the free public hot springs pool, then 30 up to Medicine Bow, and on to Casper on 487, then up Thermopolis (another good place to stop for a night) on 20 & 26 through wind river canyon (rivals any highway view in Wyoming). Take 120 from Thermopolis to Cody (it is a fairly good road we took it in our 28 ft coach last summer, though there is NOTHING on the road so start with a full tank of gas), in Cody you MUST go to the Museum of the West (ample RV parking around on the back / side), one could spend a week here and not even come close to seeing everything, it is overwhelming as a part day stop, just to walk the whole thing without stopping to look at anything might take over half a day. Heading west from Cody just after you pass through the tunnel on Hwy 14 stop at the Buffalo Bill Lake dam visitors center (they usually have shuttle golf carts running to the parking lot), it is interesting as this was one of the first concrete dams to be built in the US. See https://en.wikipedia.org/wiki/Buffalo_Bill_Dam You may consider camping out at the nearby state park if you can get reservations, this is about the last place to stay outside the park on the east side.
