Not to sure about the route that would be best, but we did Maryland to Yellowstone and back. We used KOA campgrounds because they are of a known quality, usually close to the interstate and pretty much everywhere. Though a caution, they have three night minimums on holiday weekends. Some state parks have two night minumums on summer weekends (at lease here in the East). I kept to interstates, I figured if it was designed for a semi truck, I would be ok (and was too). Still saw some wonderful country too.
HTT: "EscapeII" 2016 Shamrock 23WS (current)
PUP: "Escape" 2010 Rockwood HW 277 (gone)
TV: "Bruce" 2011 Dodge Durango V8 Hemi Crew
Just us gals (me, Sis and our daughters)
Traveled 19520 miles and 209 nights in 7 years and counting