Once you get into Wyoming on I-80, Laramie is the first interesting stop (unless you want to see Cheyenne, which is not great IMO)- some nice museums at the University of Wyoming, some interesting restaurants downtown, the old territorial prison, Snow Range mountains about 30 mins away.
The next interesting stop after Laramie will be after you get off I-80 at Rock Springs and take Hwy 191. Pinedale is nice and I suppose the gateway to Jackson Hole/Yellowstone.