We came thru Moab on hwy 191 and had a hard time googling for a campground but found that there are two in Green River, UT. One is a KOA but we stayed at the Good Same park instead just because I don't like KOA's. It was around $30 for a pull thru with water/electric. Really sparse as far as shade and grass went.
I'm not recommending it but I'm telling you that they are there. There is a lot of NOTHING for a long long way between Green River and Salt Lake City. Beautiful scenery but not much else. Be sure to Gas up in Green River. The grade isn't steep but it's a steady pull to Salt Lake City. If the wind is holding you back it's a fuel eater.
After Salt Lake City it gets sparse again real quick. NO SERVICES for miles. Everything was nice and green so the dust wasn't bad. There's plenty of smoke coming from Eastern Oregon so the air was gray north of Salt Lake City... but I did not smell smoke so it wasn't all that bad.
We just came through there four days ago.