Which character is really the tragic hero of the play?

Even though Julius Caesar is the titular character of the play, and while his death surely is a tragic one, he is not to be considered the play's tragic hero. The title of tragic hero is more fitting for Marcus Brutus.
Part of what makes Marcus Brutus such a tragic figure is the fact that he's used and manipulated by Cassius in order to carry out Caesar's death. Surely Brutus was always envious of Caesar's power, but it is Cassius's snakelike deception that causes Brutus to actually consider carrying out any violence against Caesar. Brutus cares immensely about the state of Rome, and when he is convinced that Caesar is only to become a tyrant, he chooses to act. Later, when speaking to the public about Caesar's death, Brutus suggests, "not that I loved Caesar less, but that I loved Rome more!"
He is essentially stuck between two feelings: his love and admiration for Caesar and his deep care for Rome. Torn between the two, he acts somewhat impulsively, and his actions ultimately lead to his own death. Fearful of being captured and executed in Rome, Brutus commits suicide, thus further gaining him the role of the tragic hero.