Jesus was crucified outside Jerusalem, by Romans in the Roman Empire, considered part of Rome. So yes, he was crucified in Rome
That's not what Jesus says... this is:
M,21:38 But when the husbandmen saw the Son, they said among themselves, "This is the heir; come, let us kill Him, and let us seize on His inheritance." 39 And they caught Him, and cast Him out of the vineyard, and slew Him. ...
21:45 And when the chief priests and Pharisees had heard His parables, they perceived that He spake of them.
If you force someone to do your dirty work for you, you are still held to blame; Pilate tells you this, and so does Jesus.
The Romans were tools in the hands of the Chief Priests and Pharisees (which shows you what kind of power they had), and for which Jesus never blames them; but He never stops blaming the Pharisees, en masse.
NOW, as for Jesus being crucified in Rome, what utter nonsense. No wonder people think Rome is that great city, with that sort of logic floating around.
Jesus tells us not only who to blame... but exactly where they live.
M,23:37 O Jerusalem, Jerusalem, thou that killest the prophets, and stonest them which are sent unto thee, how often would I have gathered thy children together, even as a hen gathereth her chickens under her wings, and ye would not!
And this isn't the only place He tells you it's fitting that prophets go to Jerusalem to be martyred. She is that faithless harlot, who acts like she's never been married to the God of Heaven. She is the one who teaches harlotry. When she was born, covered in blood, God cleansed her, covered her with jewels... and she took them to decorate her Idols. Yes, she did teach Rome to do these things; but Rome is a derivative, not the causation.