When we had limited time we would run to an area, look at everything we could in the area and then motor home. We too live in the East. I would strongly recommend Moab, one of my favorite spots, plan on a week, five day week which is enough to get the feel of Aches and Canyons, plus run up RT 128 out of Moab, amazing drive up and then turn around and head back. Not a long drive but well worth it. Then run down to Kanab, UT and while moving south hit Bryce, then in Kanab run over to Zion, take a tour of Best Friends Animal Society and then the North Rim of the Grand Canyon. Four days total for all that. Then run home.
Tiring, but well worth the effort and a trip no one will forget. We have done it so it's possible, this year we did it again but now retired had the luxury of two months.
Another option is Yellowstone, Tetons and then KOA at Lava Hot Springs and a run up to Jackson WY for the day, kids will love the place. Shops all over.
As for the reservations, many of our fast trips we stayed in KOAs, easy in and out, washers and dryers, good walking for exercise after a long day of driving and most are well run and clean and accept reservations. With gas as cheap as it is I suspect next summer a lot more people will be on the roads than in previous years.
Bud & Alice (Bud posts)
Abby- Black Lab-TDI Certified
Hopey-Yellow Lab-TDI Certified
2017 30' Classic
2015 F350 6.7 Diesel Crew Cab
USAF - Military Training Instructor (TI) - 68-72