"And [Paul] reasoned in the synagogue every Sabbath, and persuaded both Jews and Greeks."
The New Covenant Sabbath (which is Sunday), much like the Old Covenant Sabbath (which was Saturday), is still the first and foremost day on which everyone must be "persuaded" that Jesus is the Christ. The *place* where this happens is the church, (and, even more-specifically, the pulpit).
Once we have done our due diligence there, we are in a position to bring the gospel into the marketplace, the "Areopagus" (if you will). *Every* believer needs to be "re-convinced" of the truth of the Christian faith every week. This is because we are weak, and given to doubt and unbelief. Once we are re-energized, we are ready to be effective in God's world.
[Puritan quote of the day: "David committed many sins, but especially those two of adultery and murder, and yet God pardoned him. But Saul committed far less sins than those and yet God cast him off forever." --Jeremiah Burroughs, in "Gospel Remission"]