There is really nothing between LA and Sedona other than about 500 miles of desert. Palm Springs and Scottsdale are the two nicest desert cities and only reasonable options where you'll get comfortable accommodations and good meals.

Of course you could consider camping in Joshua Tree

EDIT: Is there any reason you couldn't return your rental car at LAX/SNA/SAN fly to Phoenix/Flagstaff/Prescott pick up a new rental car and continue on with your trip?