When you declare that one place is the world's first motel, you have to think of all the hotels that preceded it. What makes a "motel" different from a hotel? Motels cater to people traveling by car, but that seems strange, since both types of accommodations must accommodate drivers today. However, in the early 20th century, when traveling long distance by car was new, folks had to camp out because there was no place to park at a hotel. And then we pinpoint the first place that used the word "motel."
In December of 1925, the Spanish-revival doors of the Milestone Mo-Tel Inn swung open to motorists mid-way between Los Angeles and San Francisco, offering a luxurious overnight stay by any standards. In conceiving a name for his first hotel, untrained architect Arthur Heineman of Chicago, abbreviated “motor hotel” to “mo-tel” after realising he couldn’t fit all 19 letters of “Milestone Motor Hotel” on his rooftop sign.
That's how we got the word. An article at Messy Nessy Chic gives us a delightful look at how the concept of motels flourished across America, with plenty of pictures.