"But I will stay in Ephesus until Pentecost, for a wide door for effective work has opened to me" (1 Corinthians 16:8-9).
Paul always allowed the Spirit to take the lead in whatever he did. His missionary journeys were fruitful because he paid attention to God's directions, going where He led and staying as long as He said. It didn't really matter what he personally wanted; his one directive was to follow God, and he would do that regardless of the cost to himself.
At the end of 1 Corinthians, Paul mentions his desire to see the Corinthian Christians again. It's been awhile, and he wants to check in on them and see for himself how they're doing. But the time isn't right yet. He's hard at work in Ephesus, where a great ministry opportunity has come up. As useful as he would be to the Corinthians, he's even more useful to the Ephesians right now. So he'll stay put until that ministry is complete.
When Paul first set foot in Ephesus, he likely didn't have a clear idea of how long he would stay there. Some places he would stay in for years; others he would be driven out of within weeks. It didn't much matter to him; he stayed until God told him to leave. In the case of Ephesus, that meant staying there for two years until a riot drove him away.
Paul's devotion to God is striking. He wanted to be elsewhere; he could have been useful elsewhere. But he knew that there was work to be done right where he was, and he wouldn't abandon that just because he wanted to see his friends again. Nothing was more important to him than the effective spread of the good news of Jesus Christ.