There's a nice one in Hawthorne, right on the highway - Whiskey Flats. I normally stop there overnight to empty all of my tanks and winterize my trailer.
I know there are RV sites at the Fallon Campground.
There are several RV parks in Winnemucca. There really Isn't much after you leave Winnemucca. I think there are some sites behind the gas station in Orovada.
I really can't speak to any others. Home is Boise area, so once I pass Winnemucca I'm aiming for my own driveway.