It does not matter when you will both decide to get to sleep but given that it's known that you'll have to do that at some point, and then things are clearer.
One of the popular hotels is Hotel Pirat; it is 80 km from Fathiye or 130 km from Dalaman airport terminals. https://pr8Bookmarks.com/story18227905/diyarbak%C4%B1r-escort-otel