Can a 15 year old book a hotel room?

Nothing that is specifically in the law books relative to hotels/motels/inns. However, by booking a room you are entering into a contract, and that requires at least one of your party to be of legal age. Depending on your state, that will be 18 or 21. Also, some hotels will choose 21 anyway if it is the legal drinking age in that state. Beyond that, as a private business, hotels are free to set whatever other requirements they choose, except for discrimiation issues.