STORY 03 - Jewel Of The Commonwealth
Objective: Go to Diamond City
After obtaining this quest during the Minutemen quest: When Freedom Calls, a marker will appear on the map showing the location of Diamond City, the main hub of your adventuring (unless you count Sanctuary). It's a long way to travel and you'll likely run across enemies as you cross the terrain. You can approach from any direction, taking whatever path you wish. However, there's one or two things you can do to make life easier.
Investing in the Aquaboy/ girl perk which prevents you taking radiation damage in water. This is extremely useful in bypassing dangerous areas by simply swimming around them. You'll also want to approach from the North, crossing the bridge into the main area of town surrounding Diamond City. Just be warned that the streets can be dangerous as raiders and super mutants roam them. You'll see signs pointing you to the entrance of Diamond City and as you get close, friendly (or at least not shooting) security guards and turrets to protect travelers. Follow the arrows and marker until you reach the main entrance to see a lady in maroon arguing with an intercom.
This is Piper, a newspaper reporter who has been locked out of the city due to her inflammatory articles. As you approach she'll turn to you and use your presence to convince the gate guard inside to open up. After the gate opens, follow her inside. You can talk to her and/ or the mayor here (if you have decent charisma you can convince him to give you information that skips the next objective). Or you can walk right past the two of them if you like instead. You can also talk to the gate guard inside and persuade him you had no idea Piper was lying to him, getting information out of him like the mayor if you succeed.
Note: The really easy sidequest: Story of the Century is triggered here. You can complete it any time from now on to gain Piper as a companion. She will automatically join later in the story if you don't do this sidequest anyway, but bonus XP never hurts.
Objective: Find information about Shaun
Following this, you need to find some info about somebody that can help you find Shaun. Keep in mind you may need to persuade people to get the info out of them. You can talk to any of the following to find out: Artuo, Danny Sullivan, Ellie (the secretary of the detective agency), John the Barber, Moe Cronin, Nat, Pastor Clements or Piper.
Objective: Go to Valentine's Detective Agency
When you've got somebody to spill the beans, a marker will show up pointing out the location of the agency. Head down the back street and enter the place to find Ellie the secretary, who is worried about the missing detective. Talk to her about Nick, the missing gumshoe to complete this story quest and trigger the next one: Unlikely Valentine.