Adam is hanging out with Mia because he wants some closure as to why Mia stopped talking to him and ended their relationship after she went to college. Adam stayed with her during her coma after the car accident and helped her when she woke up, So it is understandable that he wants to know why she left without a word.
Adam goes to Mia's concert because he thinks it will give him closure. After the concert, one of the workers brings Adam backstage because Mia wants to talk to him. Meeting up with Mia after her show could bring Adam some closer on his previous relationship with Mia. When Mia and Adam talk after the show, Mia decides she is going to take Adam on a tour of New York City.
Adam freaked out at Mia because he wanted to know where they were going since he thought that he was being recognized by his fans. Mia called him a guy which reminded him of how they discussed "guys" when they were dating. This part of the book shows the increased tensions between Adam and Mia before the bridge scene.
Adam and Mia goes to the Brooklyn Bridge and talks about why they broke and stopped talking. Mia left Adam on the Brooklyn Bridge after she told him why she didn't talk to him anymore. After Mia walked away Adam had a breakdown and yelled into the river.
After Mia goes back and finds Adam after leaving him on the bridge, Mia lets Adam stay over at her house. They talk about their futures in music and with each other, as well as talk a little bit about the past and the accident. Mia wants to date Adam again but she is worried it won't work out because they are both busy and famous.
Adam decided that after his next tour he is leaving his band for a while and is going to go on Mia's tour with her. When Adam meets up with his band before their show he brings Mia and the band then understands why he was distant. Mia goes with Adam to his show and Adam and Mia are dating again.