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You'll find the wounded Danny Sullivan on the ramp leading to the upper stands, in front of the chapel. Talk to him to know what happened then give him a stimpak to save his life or call a doctor to tend to his wounds. Alternatively, you can have Curie take care of him if you have her as your companion.
Next, head to the mayor's office where you'll find Piper attempting to break the door down. You can pick the lock (which will be disliked by some companions, including Piper) or push the secret button under the secretary's desk.
Once the door is opened, confront the mayor. You can pass a charisma speech check to convince him in releasing his hostage. After that, you'll have the option to let him off the hook, kill him outright, or force him to stand trial (he will attack everyone). Once the issue is resolved, the quest will be resolved. For more information about various companion affinities affected by your decisions in this quest, you can check this link.