We were at the GC North Rim and then up to southern Utah last May/June and will be returning to the area in the same timeframe this year. Lots of great short hikes and awesome backroad and 4WD trails. Let me know if you'll get that far north and I can provide specifics.
I see you're from KY so I'll throw out a couple of other ideas for travelling west from eastern US (we're in northeastern NC). Palo Duro Canyon SP - Amarillo, TX. Dog Canyon Campground in Guadalupe Mountain NP - Carlsbad, NM or Brantley Lake SP for hookups. Big Bend is our favorite NP and Big Bend Ranch SP is next door with great jeep trails (3 hrs southeast of El Paso). Safe travels.