At his trial (cf. the Apology), two major charges were brought against Socrates: impiety and corruption of youth, both serious crimes with enduring consequences for the city. Impiety is a direct affront to the gods, without whose support Athens cannot prosper; corruption of youth undermines civic authority and leads to moral decay.
Without going into the merits of the case against him, the Crito concerns itself only with the results of the trial. Socrates, being found guilty, must suffer the punishment.
It is better to escape from Athens because...
Thus, we should not concern ourselves with the opinions of others; I am old and not likely to live much longer; my friends and benefactors will care for my children; death is preferable to exile because no other city is comparable to Athens; to run away from Athens is to undermine its laws and cause injury to the city; it is dishonorable to avoid one's duty; death is inescapable so why prolong life by extraordinary means?
Some of these answers are more persusive than others. The best reason, to me, is that avoiding punishment undermines respect for the laws of Athens, and invalidates a life devoted to truth and virtue. If the only way to save his life is by harming Athens, a city founded on the principles of law and justice, then the life of Socrates is not worth preserving.
The implication of this argument is that duty and honor are bound tightly to the notion of justice. And since to live unjustly requires one to abandon virtue, Socrates cannot "justify" escaping punishment. The moral force of this argument is felt by understanding that it holds true even if the punishment is unjust.
Not all of these questions are explicitly addressed in the Crito. But they are implied by Socrates refusal to leave Athens, even to save his life. The dialogue requires a deeper consideration on the role of patriotism in civic life; it suggests that duty and honor to one's country are essential, not simply for survival, but to preserve a realm in which virtue can flourish.