After the conversion of Paul, the reader again meets God-fearing Gentiles:
Act 13:14 But when they departed from Perga, they came to Antioch in Pisidia, and went into the synagogue on the sabbath day, and sat down. … Act 13:16 Then Paul stood up, and beckoning with his hand said, Men of Israel, and ye that fear God, give audience.
Israel and those that fear God are two separate groups. This is made clear when after Paul stops speaking. The Jews exit the synagogue and the Gentiles ask Paul to preach more:
Act 13:42 And when the Jews were gone out of the synagogue, the Gentiles besought that these words might be preached to them the next sabbath. … Act 13:44 And the next sabbath day came almost the whole city together to hear the word of God. Act 13:45 But when the Jews saw the multitudes, they were filled with envy, and spake against those things which were spoken by Paul, contradicting and blaspheming.
Notice that the Jews become envious. Perhaps they were used to being the main draw for converts and now an upstart preaching a new gospel gains a bigger audience then they ever could. The Jews proceed to drive him out just after Paul explains his mission to the Gentiles.
In Iconium, the reader again meets more God-fearing Gentiles:
Act 14:1 And it came to pass in Iconium, that they went both together into the synagogue of the Jews, and so spake, that a great multitude both of the Jews and also of the Greeks believed.
Paul’s primary teaching point is the synagogue. Sometimes he preaches elsewhere, when he is driven out of the synagogue or there is no synagogue. But the Gentiles primarily hear his preaching inside the synagogue.
The next God fearer that is listed in Acts is another individual, Lydia. Lydia might not be her real name but instead a name derived from the place she was from. In any case, she seems to be a Gentile in a city without a synagogue (Philippi). Lydia had worshiped God before Paul. But because of Paul “her heart was opened”:
Act 16:14 And a certain woman named Lydia, a seller of purple, of the city of Thyatira, which worshipped God, heard us: whose heart the Lord opened, that she attended unto the things which were spoken of Paul.
In Thessalonica Paul again enters a synagogue and converts Gentiles:
Act 17:1 Now when they had passed through Amphipolis and Apollonia, they came to Thessalonica, where was a synagogue of the Jews: … Act 17:4 And some of them believed, and consorted with Paul and Silas; and of the devout Greeks a great multitude, and of the chief women not a few.
In Athens, Luke seems to specify three groups of people: Jews in the synagogue, Gentiles in the synagogue and random people in the market. Notice the location change as only applied to the third category:
Act 17:17 Therefore disputed he in the synagogue with the Jews, and with the devout persons, and in the market daily with them that met with him.
Paul then goes to Corinth and again preaches to Gentiles in the synagogue:
Act 18:4 And he reasoned in the synagogue every sabbath, and persuaded the Jews and the Greeks.
source: Chris Fisher, “Jewish Proselytization and Proselytes” (realityisnotoptional).