The book takes place in the state of New York. That's really broad, though. Specifically there are three main settings in the book. The first is the jail where Steve is being kept. Steve is terrified of the jail. He is surrounded by violent criminals that use physical violence to assert their dominance. While Steve knows that he could probably act the same way, he is terrified of doing so.
The second main location is the courtroom itself. It's a popular place to make a setting of. John Grisham basically made a career out of writing about it. Even To Kill a Mockingbird sets large parts of the story in a courtroom. The courtroom in Monster stands out as being a polar opposite to the prison. Prison is wild chaos compared to the rigid structure and order of the courtroom.
The third location is revealed to the reader through courtroom testimony. That location is the section of the city where Steve lived, including the streets, the drugstore, etc.
This novel takes place in Manhatten and Harlem, NYC. One of the places this book takes place in is jail. To Steve, the main character, prison is a horrible, violent place. Prison also causes Steve to be emotionally unstable, as it reminds him of his failures. The courtroom also is where major parts of the book take place. Steve, who was accused or murder, tries to clear his name. The courtroom gives Steve a lot of anxiety, but ultimately relief when he hears that he has been given the 'not guilty' verdict. There are also flashbacks to previous scenes of his life, like his own Harlem neighborhood.