From what I can tell by reading the journal, it does not seem that they had any reservations made anywhere along the way at any type of hotel or motel. Actually, they stayed mostly at "tourist camps", which no longer really exist today, save for some that have been converted into what we call motels. Think of the little one room cabins you see in some areas (I've seen many in the northern parts of New York State), and that's a tourist camp. From the sounds of it, they just drove until they found a suitable camp and stayed there. I was particularly surprised to learn that once they got to San Francisco they had no place arranged to stay and actually had to inquire at a YMCA to find a room.
In today's world, not many people have the ability to just "wing it" like these girls did. We're such a connected society and have become so accustomed to just googling the nearest restaurant or hotel on our smartphones wherever we may be. I know I could stand to "wing it" a bit more than I do. It must have been an incredibly liberating experience for these girls to just hit the road with very few plans and take in the sites across our country as they came upon them. We all could learn a little something from them.