I think it depends entirely on if you are a destination traveler or a journey trekker! 3 weeks is a fair amount of time to see the sights at those destinations but won't allow much more than a stop over or two enroute to and from.
If I were you I'd either either make a fast trip out or back on I-80 or I-90 then slow down and "2 lane it" to or from...your choice.
Our fast route trip would be to go I-90 and be there. There are a few places to stop along that are interesting.
The more fun route is to get on hwy 20 west. It's wide open, no traffic (in Nebraska & Wyoming), scenic with small towns that nearly all have small RV parks. Don't miss the panhandle of Nebraska on the slow route...you'll be surprised our landscape isn't what some consider typical "Nebraska". (along I-80 you don't see our vast variety) You can buzz north into the Black Hills via a quiet scenic route or head into Wyoming still on hwy 20 and onward to Yellowstone on a variety of routes. We love the road north from Lusk, WY to Devil's Tower.
Experiment and mix it up...it will be a awesome trip.