I'm a lazy kitty today...
Here's from the wiki:
"The Weatherly hotel has rented rooms to Sister and Dr. Zimmer. The player may also rent a room for 120 caps off either Mr. Buckingham or Vera Weatherly. Sleeping in the bed in your hotel room grants the Well Rested benefit. Unlike other similar places in the Capital Wasteland, you often only need to rent the room once due to a bug in Vera Weatherly's script; it's effectively yours after paying. However, on occasion the script does run successfully meaning that the bed can go "red", requiring a new payment to the Weatherly in order to make the bed usable by the player. To fix this problem, just rent a bed from both Vera Weatherly and Mister Buckingham. If you do not rent from both of the hosts then it is unusable after one night.
The footlocker, filing cabinet, wardrobe, and desk in the room are all safe places to store gear.
Janice Kaplinski may enter the room and steal items lying about.
If you have any alcohol lying about, Harkness may come in and steal some, he always seems to steal moonshine if you have any lying about.
If you leave the door open when you leave, you do not have to pay to sleep in the room. It is still considered your bed."
(end of quote)
I never uses it, but I know a lot of people do.