‘But Jonah rose up to flee to Tarshish from the presence of YHWH, and he went down to Joppa, and found a ship going to Tarshish. So he paid its fare, and went down into it, to go with them to Tarshish from the presence of YHWH.'
But Jonah was unwilling to go to Nineveh and sought to evade YHWH's call by fleeing in the opposite direction to Nineveh. He did this by taking ship for Tarshish (possibly Sardinia or Spain). Tarshish (possibly meaning ‘smeltery') was the name given to a number of areas which mined the silver, tin, iron and lead carried by the ‘ships of Tarshish' (ships that carried ore, large cargo ships). Others sees Tarshish as meaning ‘the open sea', with ships of Tarshish being those large enough to cope with the open sea as opposed to sailing near land.
‘He went down to Joppa.' Joppa, or Yepu in the Amarna letters and Yapu in neo-Assyrian inscriptions, was a small port on the coast and was not in Israel or Judah. It was Jonah's first step in his attempt to get away from God. In Joppa no one would blame him for wanting to get away from Israel's influence, and from the influence of Israel's God.
This does not necessarily mean that Jonah actually thought that he could escape the presence of YHWH, only that he thought that if he abdicated his responsibilities as a prophet and left the country of his calling he would be freed from his responsibilities. YHWH's earthly dwellingplace was in Jerusalem, and Israel was YHWH's inheritance, and he presumably considered that by cutting himself off from YHWH's inheritance, the land of Israel, he could be freed from his calling as a prophet and from any responsibility to YHWH. He would no longer be responsible as YHWH's servant.
We are not told why Jonah did not want to go to Nineveh. He may well have been afraid of what they might do to a Hebrew prophet. Or he may have felt that they were foreigners, and therefore not suitable people to receive a revelation from YHWH. Or he may simply have hated Assyria because of what it had already in the past done to his people, and have felt that he wanted no part in offering them the possibility of repentance. It may be that to him they were beyond the pale. Perhaps his own family had been affected by previous Assyrian invasions. But none of these are the reasons which are made clear in the prophecy. Indeed Jonah's argument was that it was because he was afraid that he would be too successful (Jonah 4:2-3), and that YHWH might then spare the Assyrians. That would mean that his ability to prophesy the truth might then be called in question. And he emphasises that he had already made this clear to YHWH before he fled from Israel. He did not think that YHWH was being fair to him as a prophet. He could not bear to think that after prophesying the destruction of Nineveh it might not happen. What would people think about his prophetic ability then? He might even be seen as being a false prophet because what he had prophesied had not happened (Deuteronomy 18:22).
Note the threefold emphases in the verbs. He ‘rose up to flee to Tarshish', ‘went down to Joppa' and ‘found a ship going to Tarshish' (which was what he was looking for). So he ‘paid his fare', ‘went down into it', in order to ‘go to Tarshish'. In both cases what is being emphasised is his set purpose. Note also that Tarshish is mentioned three times in order to emphasise his specific destination. To most people Tarshish was the remotest spot on earth.