Tarshish had few mentions in the Bible but probably started off as a Phoenicians trading outpost.
Three men named Tarshish were mentioned early in the Bible that the port town could have been named from. Considering the ties with the Phoenicians, it's more likely that the town was named after one of Javan's sons (a son of Japheth) since the Phoenicians more than likely descended from his family line.
Jacob (Israel) > Benjamin > Jediael > Bilhan > Tarshish - 1 Chronicles 7:6-10
The Bible didn't specifically state the location of Tarshish; but, according to other sources it seems to have been in southern Spain.
The earliest references came from the King James translation in 2 Chronicles 9:21 and
20:35-37:
21. For the king's ships went to Tarshish with the servants of Huram: every three years once came the ships of Tarshish bringing gold, and silver, ivory, and apes, and peacocks.
35. And after this did Jehoshaphat king of Judah join himself with Ahaziah king of Israel, who did very wickedly:
36. And he joined himself with him to make ships to go to Tarshish: and they made the ships in Eziongeber.
37. Then Eliezer the son of Dodavah of Mareshah prophesied against Jehoshaphat, saying, Because thou hast joined thyself with Ahaziah, the LORD hath broken thy works. And the ships were broken, that they were not able to go to Tarshish.
King James also had one more place where Tarshish was mentioned - Isaiah 2:16. The remaining instances of Tarshish appeared in both King James & NIV.
The book of Psalms had a prophetic mention in Psalm 48:7 in addition to this verse about king Solomon in
Psalm 72:10.
10. The kings of Tarshish and of distant shores will bring tribute to him; the kings of Sheba and Seba will present him gifts.
Tarshish occurred in some of Isaiah's prophesies in Isaiah 23:1-14, 60:9 and 66:19.
Jeremiah 10:9 also spoke of the role of Tarshish in trade:
9. Hammered silver is brought from Tarshish and gold from Uphaz. What the craftsman and goldsmith have made is then dressed in blue and purple-- all made by skilled workers.
Three verses in the book of Ezekiel restated what Jeremiah said in Ezekiel 27 verses 12 and 25
as well as Ezekiel 38:13:
12. "`Tarshish did business with you because of your great wealth of goods; they exchanged silver, iron, tin and lead for your merchandise.
25. "`The ships of Tarshish serve as carriers for your wares. You are filled with heavy cargo in the heart of the sea.
13. Sheba and Dedan and the merchants of Tarshish and all her villages will say to you, "Have you come to plunder? Have you gathered your hordes to loot, to carry off silver and gold, to take away livestock and goods and to seize much plunder?"'
Possibly the most well-known reference to Tarshish was when Jonah "ran from God" after he was supposed to witness to the people of Ninevah. Instead of going to Mesopotamia (Babylon), he went to the coast and boarded a ship.
Jonah 1:3 and Jonah 4:2:
3. But Jonah ran away from the LORD and headed for Tarshish. He went down to Joppa, where he found a ship bound for that port. After paying the fare, he went aboard and sailed for Tarshish to flee from the LORD.
2. He prayed to the LORD, "O LORD, is this not what I said when I was still at home? That is why I was so quick to flee to Tarshish. I knew that you are a gracious and compassionate God, slow to anger and abounding in love, a God who relents from sending calamity.