A common synonym for the phrase "place rest ones head" is to use the phrase "lay down to sleep". This phrase perfectly captures the act of physically laying down and closing one's eyes to sleep. Another synonym for this phrase is to use the phrase "hit the hay". This phrase is informal and playful in nature, making it a great option for casual conversations or situations where you want to be lighthearted. The phrase "crash" is another synonym that is often used for the act of sleeping. It can convey a sense of suddenness or urgency when describing the need to sleep.