How to unlock: The quest gets unlocked when you complete An Unlikely Valentine - after you rescue detective Valentine and you both go back to Park Street Station (M6,5).
- Go to Valentine's agency
- Talk to Ellie
- Sit down
- Tell your story to Nick
- Follow Nick
- Obtain the key to Kellogg's house
- Search Kellogg's house
- Show the cigar to Dogmeat
Return to Valentine's office
You need to go back to Diamond City Market and head for Valentine's office. Start by talking to Ellie. You will receive Faded Trench Coat, Worn Fedora and bottlecaps (100 or more if you persuaded Ellie to set a reward for rescuing the detective). You can sit in the chair now, then tell Nick Valentine your story and describe Shaun's abduction. The detective will offer to help investigate Kellogg's apartment, since he suspects him of taking part in the abduction.
Follow Nick to Kellogg's house
Get out of the office and follow Nick Valentine. He will lead you to Kellogg's apartment located in the Diamond City Market. When you reach it, you'll see a locked door and you'll have to solve the issue.
Gaining access to Kellogg's house
You can gain access to Kellogg's house in two ways. The first one is using a hairpin to unlock the door. It is possible only if you developed the Locksmith perk up to at least third level that will allow you to open Master locks.
If you don't have the required skills, you have to acquire the key. To do so, go to the Mayor of Diamond City, whose office is located above the market. Find the elevator near the market exit - it leads to the Mayor's office. Stand inside, press the red button and wait until you reach the top. You'll see Piper (if she's not your current companion) and you can have a brief conversation with her to see why she wants to meet the Mayor.
You can get Kellogg's house key from one of two people - one of them is Mayor McDonough. He will refuse to give you the key but you can bribe him with 250 bottlecaps or use Charisma and convince him that Kellogg is the abductor. Alternatively, you can pickpocket him (high stats and corresponding perks are required).
Another person who has the key is the Mayor's secretary, Geneva. While talking to her, you can act similarly - give her 250 bottlecaps as a bribe or use one of two dialogue options available if you have a high level of Charisma.
Regardless of how you obtained the Kellogg's House Key, bring it back to Valentine and use it to open the door.
Searching Kellogg's house
Kellogg's apartment is not a big one and you don't even have to enter the upper floor. Stay on the first floor and search the desk. There is a button shown in the screenshot above; pressing it will unlock a secret chamber.
Of course, you can collect all items from the secret room. The crucial step is to pick up the Cigar Box and Gwinnett Stout from the table near the chair. Listen to the conversation with Nick about using Dogmeat's sense of smell to determine Kellogg's location. You can now decide whether you want to take Valentine or your current companion with you (the choice will not affect the quest too much).
Showing the cigar to Dogmeat
Exit Kellogg's apartment. Dogmeat should be waiting close to the building. You just need to get close to him and show him the cigar. You'll take care of finding Kellogg during the next quest - Reunions.
Rewards for completing the quest: Experience points, a new quest (Reunions).