Unlikely Valentine

Unlikely Valentine is a main quest and achievement/trophy in Fallout 4.

Quick walkthrough
Upon following the advice of Diamond City locals, the Sole Survivor sets out to the detective agency, only to find Nick Valentine is missing. Ellie Perkins gives the Sole Survivor the quest.

Detailed walkthrough
After speaking to Ellie Perkins, it is revealed that Nick Valentine is being held captive in Park Street station. The station is filled with feral ghouls, but inside the station is the entrance to Vault 114. The vault is guarded by Triggermen armed with sub machine guns. The player needs to fight their way through the vault until they come to a large open Atrium. Upstairs is Dino guarding the Overseer's office where Nick is being held. Sneaking close allows the player to listen to a conversation between Valentine and Dino where Valentine convinces Dino that a crime boss is upset at him about his gambling habit. Dino then runs out of the room to square things off with said crime boss leaving the coast clear to free Valentine. Alternatively, Dino may be killed without waiting for him to leave. The control panel next to the office door can then be used to free Valentine.

Speaking with Nick reveals why he is there and that they should leave as soon as possible. On the desk behind him is the Speech bobblehead. After talking with Nick he will lead you out of the vault where you will be stopped by Skinny Malone and Darla. With a few speech checks it is possible to turn them against each other or leave the vault without fighting at all. If a certain stage of the quest The Sight with Mama Murphy has been completed before coming to the vault, there will be an additional speech option that will allows escape without any violence. Otherwise, the Sole Survivor and Valentine will need to kill Skinny Malone and his companions in order to leave.

After exiting the vault there is a short conversation with Valentine where he directs you to meet him back at his office in Diamond City. Upon arrival, speaking with Ellie will end the quest.