264 is a nice drive and the route you’re talking about is only 150 miles or so. You can get fuel in Tuba City but in between is pretty sparse so I wouldn’t launch without a full tank.
Since you’re in the area I’d recommend taking a trip up to Monument Valley if you haven’t been there before. There’s RV camping at Monument Valley but there’s also a little known spot north of there just outside of Mexican Hat Utah called Goosenecks State Park. It’s primitive camping and there is no fee but the views are unlike anything you’ll experience back east. It makes a nice jumping off point for touring the area.