To begin this quest, speak to Vadim Bobrov at the Dugout Inn. He's good friends with Diamond City Radio's DJ Travis, but he really wishes that Travis was more confident. He wants you to help encourage Travis somehow. Your next step is to wait until 6 p.m., which is when Travis usually visits the Inn.
When you return, you'll find a greaser named bull harassing Travis. Use that opportunity to build up Travis' courage. It also helps to tell him that you have his back. Travis and Bull will fight, leaving you to take on Bull's partner. It's not much of a fight, and the result will set Travis on the path to higher self-confidence.
Vadim would like to take this scheme one step further. This time, he wants you to play matchmaker. Both Travis and the Inn's waitress, Scarlett, have been eyeing each other, but neither of them are willing to make the first move. You can find her at either the Inn or close by within Diamond City. Speak to her and select conversation choices that will encourage her to introduce herself to Travis.
Return to the Dugout Inn and speak to Yefim. You'll learn that, while you were away, Bull kidnapped Vadim. While you're probably capable of taking Bull and his buddies all by yourself, this is a prime opportunity to take Travis along to boost this confidence even more. Head to the radio station using the quest marker, and let Travis know of the situation. Then fast travel to the Beantown Brewery, where Travis will be waiting for you at the entrance.
Make your way to the latest quest marker (Vadim) by going up the ramps and on the catwalks, taking taking out Bull and his goons along the way. You'll find Vadim in the office. Free Vadim and speak to him. Then speak to Travis to complete the quest.