As soon as you load your game, you'll get this quest active. Open your Pip-boy and listen to the Valentine's Detective Agency Radio. After listening to Ellie's message, travel to Valentine's detective agency in Diamond City to talk to her. After that, you can bring Nick with you and travel to the Coastal Cottage then walk to the far to the NE of the Commonwealth to locate the Nakano residence. (Note: Nick Valentine is not required to do this quest. In fact, you can do it alone if you want to)
Once you reach the house, get inside and talk to Kenji. After talking to him, you can question the couple to start your investigation. You can go upstairs and investigate Kasumi's room. In the hallway, you can find a holotape (Kasumi's Projects: Lamp). Inside her room, you can pick up another holotape under her bed (Kasumi's Projects: Dreams) and her journal behind the toolbox on the drawer beside the bed. Finally, the last holotape in the room is found on her table in the corner. (Kasumi's Projects: Radio)
Leave the house and go to the boathouse near the house. There's an Expert safe beside the boat and the Grandfather's note on top of it. You can brute unlock the safe if youre lockpicking skill is high enough. Otherwise, examine the picture frame on the table nearby to find a hidden key. Use it to open the safe. Loot the contents then play Kasumi's final holotape. This will update your quest objective. Talk to Kenji to update the quest. You'll receive 300 caps as initial payment.
You'll have to travel to Far Harbor next. If the Brotherhood and the Railroad is still active and you're affiliated to them during this point of the game, you'll have the option to tell them about the Synth Refuge.
(Optional: Tell the Railroad about the Synth Refuge: Talk to Boxer in Railroad HQ)
(Optional: Tell the Brotherhood about the Synth Refuge: Talk to Kells in the Prydwen)
Make your preparations then travel to Far Harbor when you're ready. The area will be a separate map from the Commonwealth but you'll have the capability to fast-travel from there and back. Make sure to bring high-rad resistance equipment or power armor. You can also bring a companion for this quest. Upon reaching the dock, the quest will be complete.