Why was Paul eager to visit Spain (Romans 15:24)?
Recall that he viewed himself as the "apostle to the Gentiles" (Romans 11:13). Paul often quotes the prophet Isaiah in relation to the Gentile mission. But sometimes he only alludes to Isaiah. One such allusion is to Isaiah 66:18-20:
“For I know their works and their thoughts; the time is coming to gather all nations and tongues. And they shall come and see my glory. I will set a sign among them and will send survivors from them to the nations: Tarshish, Put, Lud, Meshech, Tubal and Javan, to the distant coastlands that have neither heard my fame nor seen my glory. And they will declare my glory among the nations. Then they shall bring all your brethren from all the nations as a grain offering to the LORD, on horses, in chariots, in litters, on mules and on camels, to my holy mountain Jerusalem,” says the LORD, “just as the sons of Israel bring their grain offering in a clean vessel to the house of the LORD.
Tarshish, Put, Lud, Meshech, Tubal, and Javan are countries that can be located on a map, even though they may not be familiar to the modern reader. At the first Christian Pentecost (30 AD), Jews converged on Jerusalem from the diaspora (the dispersion that resulted from the exiles God used to discipline his people), including the nations referred to in Isaiah 66.
As they returned to their nations of residence, Gentiles all over the Mediterranean had a chance to be included among God's holy people. At the time Paul wrote Romans, the gospel had been taken to all the lands Isaiah mentioned -- except for one: Tarshish (Spain). Truth be told, there are multiple suggestions as to the location of this Tarshish, since there is apparently than one candidate for purposes of identification. But this is at least a worthwhile possiblity to contemplate.
At the very least, all agree that Paul was willing to go to the ends of the earth (Acts 13:47; see 2:39). His action in doing so was necessary for the completion of the Gentile mission. Thus his zeal to visit Spain.