Crito
The dialogue takes place in Socrates' prison cell, where he awaits execution. He is visited before dawn by his old friend Crito, who has made arrangements to smuggle Socrates out of prison to the safety of exile. Socrates seems quite willing to await his imminent execution, and so Crito presents as many arguments as he can in order to persuade Socrates to escape. On a practical level, Socrates' death will reflect badly on his friends--people will think they did nothing to try to save him. Also, Socrates should not worry about the risk or the financial cost to his friends; these they are willing to pay, and they have also arranged to find Socrates a pleasant life in exile. On a more ethical level, Crito presents two more pressing arguments: first, if he stayed, he would be aiding his enemies in wronging him unjustly, and would thus be acting unjustly himself; and second, that he would be abandoning his sons and leaving them without a father.
Impiety
The issue of impiety in antiquity is very controversial because of the anecdotal nature of extant sources. A number of Athenian men, including Alcibiades, were sentenced to death for impiety in 415 BC, most of whom fled Athens before execution (Andocides was later charged in 400 or 399 BC in reference to these events). Most famously, the philosopher Socrates was executed for impiety (as well as corrupting Athenian youth) in 399 BC. An Athenian philosopher Anaxagoras taught that the sun and the stars were fiery stones whose heat we did not feel because of their distance, and was allegedly accused of impiety in Athens. Diagoras of Melos was reportedly accused of atheism and had to flee Athens after being charged with impiety for revealing the content of the Eleusinian mysteries to the uninitiated. Philosophers Aristotle and Theophrastus might have been accused of impiety as well.