Start the quest at the Valentine Detective Agency, then speak to Nick's assistant. With Nick Valentine rescued, now is the time for him to hear your case, so please have a seat. He's a detective so this is when you give him all the background information on Shaun's kidnapping. He will deduce the next step: talking to fellow Diamond City resident Kellogg. Follow Nick out of his office for a walk over to Kellogg's residence.
It turns out Kellogg hasn't been at his place for a while. With no additional leads, you have no choice but to break into the guy's place. If you have a Master level Locksmith perk, you can get through the door. Otherwise, you can get a key from the mayor's assistant. Head in the direction of the chapel near the entrance of Diamond City and follow the arrows and signs to the mayor's office. You might find Piper in a disagreement with the assistant. After they're done talking, talk to the assistant and explain your situation. To get a copy of Kellogg's key, you can either try to charm the assistant and the mayor or bribe the assistant with 250 bottle caps. Whatever you decide, head back to Kellogg's home once you pick up the key.
With Nick Valentine in tow, this scene is a game of classic clue-hunting. Like a scene out of a detective movie, the trick involves pressing the hidden switch under the desk, revealing a hidden passage. You can continue to search for clues on your own, but if you want to save time, grab the cigar, which is the clue needed to conclude the quest. You'll come to the conclusion that Dogmeat needs to sniff the cigar to find the trail. Assuming you met Dogmeat near the beginning of the game at the Red Rocket south of Sanctuary Hills, the dog will be waiting for you outside Kellogg's place.