This is a companion quest that will be initiated by Nick once his affection level towards you has increased significantly. For this quest, you need to hunt down 10 Eddie Winter holotapes to get the code to open his shelter.
Once you have all the tapes, give them to Nick. Take note that handing over the tapes will temporarily remove Nick as your companion so take whatever you need from him for the meantime. Travel to Andrew Station beside the South Boston Police Dept and meet up with Nick.
Head to the location and kill off the raiders. Head downstairs to enter the station itself. Inside, make your way north, then enter the Hole in the Wall. Follow the straightforward path until Nick leads you to Eddie's bunker's entrance.
Let Eddie and Nick talk to each other. Once done, kill the *******. Also, don't forget to loot his unique gun, Eddie's Peace. There's also an Expert Safe and Expert terminal in the room. The terminal is used to open the safe. The holotape, “To Claire” is found on the cabinet beside the bed.
Head outside and continue to the next room, what seems to be a bar. There's a named raider there called Chancer. Kill him then find the hidden button behind the cabinet to open the security door. This gives you access to the steamer trunk and chem station inside. Go upstairs and and grab Joe Spuckie's basement key. Use the ladder to exit to the Joe Spuckie's sandwich shop.
Follow Nick outside and approach him to complete the quest and to maximize his affinity towards you. You'll get his “Closer to Metal” perk after this.