Roman Sparta was made a free city in the Empire, but remained a dictatorship locally. There was no direct land route to Corinth; at least, none that was easily passable. These are all some of the reasons why Paul's second journey did not take him beyond Corinth. By land, there was virtually no place to go. By circumstance, there was no immediate link within Paul's larger strategy. Geographically, Corinth was an isthmus, but in terms of making one's way through the civilized world, Corinth was basically the end of the road in Achaia.
Of course, Paul had both short and long term views, about strategy. About six years after he first walked into Corinth, Paul had been as far west as Illyricum, but Paul had still not traveled outside of the old (pre-146 BC) Achaian League territories. He'd just helped plant a church in Rome, from far away, but Paul had avoided the hinterland of each major city. Thrace, Lycia, northern Galatia, and the Peloponnese were still outside the limits of what Paul had been able to reach himself, to that point. But Paul had greater hopes to accomplish much more, in time, through his churches.
[W]e were the first to come even as far as you in the gospel of Christ... with the hope that as your faith grows, we will be, within our sphere, enlarged even more by you, so as to preach the gospel even to the regions beyond you, and not to boast in what has been accomplished in the sphere of another. (2Cor.10:14-16)That word sphere ('kanwn') in this context means limits, rules or boundaries. In this case, it may as easily mean "province" as "sphere". That in turn may mean, according to Paul, that the church in Corinth was eventually supposed to evangelize its own backyard. Through them, Paul hoped, his reach would be extended. For Paul, this regional strategy was limited and yet unlimited.
Paul's feet never touched the Peloponnesus, so far as we know. But his heart did.
Chronological footnote: Partly, I said all that to say this. For Paul, "beyond" Achaia wasn't west to Illyricum - a poor reason why some argue that 2nd Corinthians belongs earlier in Paul's travels. For Paul, as for the vast majority of all Greeks everywhere, the region "beyond" Achaia was the Peloponnese.