To my mind, Cassius is the villian of the play. He initiates the central conflict of the play, brings about the death of Caesar and Brutus, and most importantly turns Brutus against himself.
There is a similarity shared by Julius Caesar and MacBeth regarding questions of characters' formal roles as being the protagonist, villain or possibly both.
In each case, we have a central character who has been convinced to commit a crime and second character who initiates that crime, which in both cases is an act of betrayal (political and self betrayal). Lady MacBeth, like Cassius, can be seen as the "real villian" of the play because without her there would be no first act of evil. There would be no sword stroke.
Cassius too is instrumental in creating the evil act which is committed by the protagonist, Brutus.
Marc Antony is the real villain. For, he professes love for Caesar and love for Rome, yet he exploits Caesar's death inciting the Romans to the most damaging of wars, a civil war. On the battlefield he casually discards the life of his nephew for his own gain, and he becomes embroiled in conflict with Octavius Caesar, the nephew of Julius Caesar, and part of the triumvirate. Ironically, Marc Antony becomes guilty of the very cupidity of which he has accused Brutus and the other conspirators.
No, Brutus is certainly not the villian. A villain must be someone who intentionally tried to harm for purposes that suit their own needs. While many may have been disappointed in Brutus' decision to join the conspirators, his intentions were clearly to do what was the best for Rome. He had a high position as a senator in Rome and was respected by people everywhere. Joining in the conspiracy to join Caesar could only jeopardize his prestigious position.
Some may say Caesar is the villain, though Shakespeare seems to hedge readers towards thinking it was Cassius. That debate can go on and on, but with Brutus' good intentions always at the forefront, it is hard to label him as the villain.
In Shakespeare's Julius Caesar, Brutus serves as the protagonist. He is the tragic figure. Loyal followers of Caesar might call him a villain, but in general, readers do not think of him in that way.
Antony's words at the close of the play explain why: Brutus does what he does for a noble cause. He is noble in a broad sense, and is motivated by what he thinks is best for Rome. He doesn't join with the conspirators to assassinate Caesar out of jealousy or the desire for personal gain. He joins the conspiracy because he is afraid Caesar will become a tyrant, and that would be bad for Rome. Brutus may be mistaken, and he certainly is a terrible decision-maker, but he is not a villain.
Notice, for instance, that Brutus fails and falls, not because he assassinates Caesar, but because he makes bad decisions. In short, he falls because he doesn't listen to Cassius, who, by the way, is a villain. If the villain Cassius were in charge (and Antony killed along with Caesar as Cassius suggested), the conspirators would have won. It hardly seems possible that Shakespeare is condemning Brutus as a villain when Brutus would have survived and ruled if he had listened to the obvious villain.
No, Brutus may be foolish and naive and certainly makes bad decisions. But "villain" isn't a word often used to describe him.