Tons of places along I70, and Moab I believe is basically in the middle of BLM land. You could also ask some of the Grand Junction guys for suggestions.

I wouldn't go shooting anywhere truly in the immediate area around Moab during EJS week, or off any of the main trails. Too many people camping, hiking and wheeling. You never know when someone will be coming right around the corner. But I doubt you'll have any problems finding a place. You could call the Moab information center and they'd probably have some suggestions for you, but once you make the drive you'll know what I'm talking about.

Make sure you read up or ask about the cryptobiotic soil - you don't want to walk or drive on that stuff as some of it takes hundreds of years to grow back.