Fallout 4 Player Character Housing

Ownable housing
These homes are considered owned by the player upon meeting a certain condition such as a payment or quest completion, note that you cannot send companions to owned player houses, only settlements.
 * Home Plate, if the Sole Survivor purchased the house from Geneva for 2000 caps.
 * Vault 81 room, if the Sole Survivor completed the quest Hole in the Wall by giving the cure to Austin.
 * The Prydwen Quarters, if the Sole Survivor joined the Brotherhood and has the rank of Paladin by completing Blind Betrayal.
 * The Institute Director's quarters, if the player joined the Institute and completed Nuclear Family, upon completion of the quest the player will be informed that the quarters are theirs, although the bed in the Director's quarters is not usable and the room that the synth Shaun resides upon the first visit is still inaccessible to the player.
 * The Institute player's quarters, if the Sole Survivor joined the Institute and completed Synth Retention. This room is located on the 2nd Level of the tower with the balcony that connects to the elevator.
 * The USS Constitution Captain's quarters, if Ironsides is visited after the completion of Last Voyage of the U.S.S. Constitution. (Note, Completing the quests only makes the bed usable, ALL items in the Captain's cabin are still considered owned)
 * Listening Post Bravo, if the player completes Blind Betrayal for the Brotherhood of Steel the location will gain some workbenches and a bed, the Listening Post can also be used as a base if the Sole Survivor hacks the terminal and kills the yao guai that resides inside if the Sole Survivor sides against the Brotherhood.

Far Harbor

 * A room can be rented from Mitch in The Last Plank for 10 caps.

Nuka-World

 * Both the interior and patio of Fizztop Grille can be used for player housing after becoming overboss.

Creation Club Housing

 * Neon Flats
 * Shroud Manor
 * Charlestown condo
 * Noir penthouse

Hotels and rentable housing
The locations listed below will allow you access to an Unowned Bed if you pay a specific amount to a certain NPC at that location, the bed will become owned again after a certain amount of time.
 * Dugout Inn
 * Hotel Rexford
 * Bunker Hill

Incidental housing
The houses below aren't technically owned or paid for but the Sole Survivor can still seek shelter in these locations:
 * Combat Zone: After killing all of the raiders in the Combat Zone and gaining Cait as a companion, the raiders will no longer respawn, allowing the Sole Survivor to use the Combat Zone as a player home. It is unconfirmed whether the containers in the Combat Zone are safe or not.
 * Diamond City Wall Room: With a power armor jetpack or careful use of jet, the Sole Survivor can find a secret room on top of the exterior wall of Diamond City, down the right alley from the main gate. The room contains a power armor station and an unowned bed; it is unconfirmed whether the containers are safe but it is confirmed that the power armor station is safe to store items in. This is an inconvenient location due to the difficulty of getting to it.
 * Kellogg's house: After gaining access to Kellogg's House you can use it as a place to store items and sleep in, as the location does not reset so all containers are safe. The beds in the house are also free to use.
 * Vault 111: After getting the Pip-Boy you can use Vault 111 as a player home because it does not reset. It is useful due to its close proximity to the settlement of Sanctuary Hills.
 * Railroad HQ: If you join the Railroad you can use the Railroad HQ as a player home. The HQ has all the workbenches and is inhabited by a doctor and a merchant.
 * The Castle tunnels: After completing Old Guns you can use the tunnels underneath the Castle as a base because it does not reset.