In Plato's Phaedo, the Socratic dialogue that occurs in the hours leading up to Socrates' death, his student Phaedo says the following:
"Then tell me, Socrates, why is suicide held not to be right? as I have certainly heard Philolaus affirm when he was staying with us at Thebes: and there are others who say the same, although none of them has ever made me understand him. " http://classics.mit.edu/Plato/phaedo.html
So it seems that Socrates had friends or students in Thebes, at least at one point. Obviously the political situation changed during the war so Phaedo might be referring to happier times when travel to Thebes was more viable, but I don't know.
My understanding is that exile for a normal person was often a death sentence. Being a free man without a home was arguably worse than being a slave. At least a slave has a place. You can't just murder a slave without repercussions (paying back the owner). Xenia wouldn't really apply to an exile (I doubt) since he isn't able to reciprocate any sort of gift-giving. And it's not like the economies of contemporary cities were mature enough that an exile would likely have any sort of marketable skills, he probably owned a small farm and now has no land. Mercenaries or rowers might be an exception to this (persons with marketable skills).
All that said though, Socrates was a celebrity. Plato and Aristotle both were coveted tutors to the elite, Plato in Syracuse and Aristotle for Alexander the Great in Macedonia. I have a hard time imagining that there wouldn't be many people who would have happily been patron to an exiled Socrates, either as a tutor for themselves or or their children, or just to be the coolest guy at the symposium.
Good candidates would be northern Peloponnesian states (definitely not Sparta) such as Corinth, or Magna Graecia (Sicily or southern Italy), as these areas were fairly receptive to Athenian exiles; Thebes, suggested by /u/AllUrMemes, is also a good idea.
(I have no idea where the_crustybastard got the bizarre notion that Sokrates was prosecuted for being pro-Spartan. No evidence pointing that way exists. It's certainly not sustainable by pointing to Sokrates' war record in the battle of Potidaia, where he fought against Spartan interests.)
The core of the official charges against Sokrates appears to have been asebeia, "impiety", which became a prosecutable charge in 432 BCE. Here's what other people charged with the same offence did:
As to motives behind the trial: broadly speaking we have indications of two basic motives for the prosecution. The first is the tradition given by Sokrates' followers: Diogenes Laertios (who is not in himself reliable) claims to give the exact wording of the charges as follows:
τάδε ἐγράψατο καὶ ἀντωμόσατο Μέλητος Μελήτου Πιτθεὺς Σωκράτει Σωφρονίσκου Ἀλωπεκῆθεν· ἀδικεῖ Σωκράτης, οὓς μὲν ἡ πόλις νομίζει θεοὺς οὐ νομίζων, ἕτερα δὲ καινὰ δαιμόνια εἰσηγούμενος· ἀδικεῖ δὲ καὶ τοὺς νέους διαφθείρων. τίμημα θάνατος.
Meletos son of Meletos, the Pitthean, brought he following charge and swore to it against Sokrates son of Sophroniskos, the Alopekian: Sokrates commits injustice by not recognising the gods that the city recognises, and by introducing new divinities; and he also commits injustice by corrupting the young. Penalty: death.
The second indication comes from a mid-4th century orator, Aischines, who was not a disciple of Sokrates or his followers. In his Against Timarchos 173 he reports that the Athenians
killed Sokrates the sophist, because he was shown to have been the teacher of Kritias, one of the Thirty who destroyed the people.
Kritias was the most notorious of the Thirty Tyrants who ruled Attica briefly in 404 BCE, murdered between 5% and 15% of the citizen population and seized their property for themselves, and appointed "whip-bearers" to keep the rest in line. He was closely associated with Sokrates and appears in some of Plato's dialogues, and there is fairly decent evidence to suggest that he was also known for his atheism.
It seems likely, on the available evidence, that the official charge was as Diogenes Laertios reports (the reports in Plato and Xenophon are completely consistent with his wording), but that the real motivation for the trial was his close association with Kritias' appalling crimes. There was no way they were going to let him go: doing that would be comparable to letting Goebbels off scott free.
Sparta.
The whole reason Socrates was finally prosecuted was due to his pro-Sparta ideology.
The two records we have about of Socrates were written by his devoted fanboys: Plato and Xenophon. Neither should be read as presenting solid, dispassionate history — they're both writing works of pro-Socrates advocacy. And it cannot be said they do anything besides placing Socrates in a very positive light, so in that regard, they're extremely successful.
However, they certainly don't put Socrates in a very accurate light.
In Athens, Socrates was regarded as a war hero, having performed some heroics at Potidea. Before Athens went politically to shit, he was the city's generally tolerated resident eccentric. This is not to say he wasn't mocked as a sophist and grifter who trained young men in those base arts. (See Aristophanes' The Clouds).
But Socrates' obsession with Sparta and all things Spartan (and contempt for Democracy) eventually became pretty grating to his neighbors, who were suffering under a heavy boot of Spartan occupation and oppression. Nor did it escape his neighbor's notice that Socrates was closely associated with some of the most despicable members of the pro-Sparta government installed in occupied Athens — particularly the infamous Critias.
Check out Professor Doug Linder's "Famous Trials" site on Socrates. http://law2.umkc.edu/faculty/projects/ftrials/socrates/socrates.htm
Read the I.F. Stone interview. Stone does a nice job addressing the apparent contradictions and providing the context of the prosecution.
According to Crito in Plato's Crito, Socrates could have gone to Thessaly:
And do not be troubled by what you said in the court, that if you went away you would not know what to do with yourself. For in many other places, wherever you go, they will welcome you; and if you wish to go to Thessaly, I have friends there who will make much of you and will protect you, so that no one in Thessaly shall annoy you.
(45b-c).
He could have headed off to one of the Greek colonies in Magna Graecia (Southern Italy) or even further, perhaps Massalia in southern France would have taken him. Certainly, we hear about Greeks who retired to the Greek colonies. A small, non-judgmental community outside Greece could have been his best bet.
Would Roman Republic (under Marcus Furius Camillus if I did not miscalculate) be a viable option?