Today is the Ides of March!
As a long-time amateur student of ancient Roman history, I think we sometimes overlook how the conspirators succeeded in their immediate objective of killing Caesar, but failed miserably in their ultimate objective of restoring the Republic. Indeed, on the latter front, they actually made things worse.
Within just a few years of Caesar's assassination, almost all of the conspirators were dead, having been defeated by the Caesarians led by Mark Antony and Octavian.
The new regime of the triumvirate (Antony, Octavian, and Lepidus) was actually much MORE authoritarian and repressive than Caesar had been. Antony and Octavian decided Caesar's big mistake was being too nice to his enemies (he famously spared almost all of them, refrained from confiscating their property, allowed them to hold public office, etc.). They "fixed" that error by instituting massive proscriptions that killed thousands of people. When, after another decade of intermittent warfare, Octavian finally emerged as the sole ruler of Rome (renaming himself Augustus), the Republic was far more thoroughly dead than it had been under Caesar.
Where did the conspirators go wrong? A very incomplete list:
Letting Mark Antony live was an obvious error (Shakespeare got that one right).
It was also a mistake (though a less obvious one) to trust Octavian. In fairness, it was hard to predict that a 19 year old would turn out to be such a formidable adversary.
More generally, the conspirators failed to sufficiently consider that there was a large and powerful Caesarian faction in Rome, with widespread support among both the elites and the masses. These people were never going to simply roll over and accept the restoration of the old Republic. It was never a simple matter of just getting rid of one man (Caesar), after which everything would go back to "normal."
Along similar lines, the conspirators had no real plan for restoring the credibility of the old regime in the eyes of those who had come to reject it. Neither did they have a plan for suppressing the inevitable resistance to their rule (they did not have any equivalent to the reign of terror ultimately instituted by their adversaries).
In fairness, the conspirators also had some bad luck. The two consuls they and the Senate left in place (Hirtius and Pansa, initially nominated by Caesar) were killed in battle against Antony (after defeating him), allowing Octavian to take over their army. Maybe things would have gone better for the restorationists if one of the consuls had survived. But Octavian (Caesar's official heir) was going to find a way to assert himself, regardless. And Hirtius and Pansa were actually Caesarians themselves (Hirtius even authored parts of Caesar's memoirs).
What should the conspirators have done differently, beyond offing Antony and Octavian as soon as possible? I honestly don't know. The challenge they took on was much greater than they expected. Maybe they could have somehow prevailed through a combination of better luck and better strategy. But maybe the Republic was simply too far-gone to save.