We generally looked to get to most places by 7pm. If I recall something along these lines...
Litchfield - just after 7pm (made it to the Ariston at 7.50pm they close at 8pm)
Lebanon - again just after 7pm
Edmond - about 9pm (long driving day)
Amarillo - about 8pm
Albuquerque - very early, about 5.30pm
Holbrook - 4pm ish
Grand Canyon - 4pm ish again
Kingman - 6-7pm ish
I think you'll be fine to just turn up at most places. In each of these places there were several alternatives available in the event of no vacancies.