It is often thought that Luke was from Troas because the first person plural begins there (Acts 16:10-11). However, the start of the 'we passages' does not correspond to the start of Luke's presence with Paul. We have seen here that Luke (=Lucius) was with Paul in Corinth, yet the first person plural starts only at Acts 20:5-6. The switch to first person narrative occurs, not when Luke joins the party, but when the party (including Luke) sets sail. It is no coincidence that every "we passage" begins with a sailing (Acts 16:9-10, Acts 20:5-6, Acts 21:1, Acts 27:1). Vernon Robbins is right that Ancient writers preferred to use the first person for sea voyages (see here), (though his suggestion that the person behind the "I" need not have been present has been rightly rejected). Therefore Luke can have joined the missionary group at any time before the departure from Troas (Acts 16:9-10). The view that Luke was from Troas is problematic because:
a) Acts 16:6 tells us that the holy spirit had forbidden Paul from preaching in Asia. Luke could not have written this if he had been converted through Paul's preaching in Troas, which is in Asia. The two further pieces of divine direction in Acts 16:7-10 similarly have the purpose of getting Paul and his companions to Europe without delay. The implication is that the missionaries did not linger to preach until they got to Europe.
b) When Paul later preached in Troas he did not know whether a door would open for him (2 Cor 2:12-13) and this further suggests that he had not attempted to preach there before. See my blog post here.
c) Chronology does not allow time for extensive preaching in Asia (or indeed during a hypothetical trip to north Galatia). Paul's visit to Jerusalem (Acts 15) cannot have been earlier than 48. The Gallio incident can be dated to 51 (for all the usual reasons and because the probable food shortage in that year is likely the cause of the urban unrest that resulted in the beating of Crispus-Sosthenes). Paul's arrival in Corinth can therefore be dated to early 50 at the latest. Therefore we have two years or less for the events of Acts 15:1-18:1, which included a trip to Jerusalem, "some days" in Antioch (Acts 15:36), a visit to the south Galatian churches, the evangelization of Macedonia and Athens, and lots of walking. Little time can be allowed for preaching in Asia.
d) Paul's travel companions were always experienced believers whom he had known for some time. Consider Barnabas, John-Mark, Silas/Silvanus, and Titus-Timothy. If Luke was from Troas he would have become a travel companion of Paul within days of first meeting him, and there is no precedent for this.
The evidence that the author of Acts was from Antioch is as follows:
1. He was a part of the mission team that evangelized Europe (Acts 16:11). Antioch was the point of departure for this mission, (Acts 15:40). Paul was a resident of Antioch, and there are good reasons to suppose that Timothy was also from Antioch (whether or not he was Titus). Silas was also known in Antioch.
2. I have argued that the author of Acts was Lucius/Luke. Lucius of Cyrene was one of the "prophets and teachers" in Antioch (Acts 13:1). He has the right name and sufficient prominence to have been the Lucius of Rom 16:21. He was evidently one of the "men of Cyprus and Cyrene who, on coming to Antioch, spoke to the Hellenists also, proclaiming the Lord Jesus" (Acts 11:20). He was therefore probably a preacher to non-Judeans and this would make him a likely companion of Paul on the second missionary journey.
Dunn and Jewett have suggested that the Lucius of Rom 16:21 is not given a very full description and therefore cannot have been Lucius of Cyrene, an important figure in Antioch. However, they fail to account for the importance of name order in the ancient world. Paul indicates Lucius's prominence by placing him second of the eight who send greetings in Rom 16:21-23. Also, Lucius, Jason, and Sosipater were about to deliver the collection, and this was illegal (see here), so a full description might have identified them too precisely and thus endangered them.
Others assume that the author of Acts would not have mentioned himself by name. But why not? The writers of Luke-Acts and the other gospels deliberately did not identify themselves, but that does not mean that the genre required that they not name themselves. Indeed, the gospels of Matthew and John were soon attributed (rightly or otherwise) to characters named in their texts. Furthermore, Josephus generally refers to himself in the third person as "Josephus". The writers of Matthew, Mark, John, and Luke-Acts leave themselves unidentified in conformity to a style of Jewish literature that goes back to the old testament history books (so Baum Nov Test 50 (2008)). By leaving themselves unidentified they kept their readers' focus on the narrated events. It seems to me that this style does not require that the author not write about himself: it requires only that he not identify himself.
3. At Acts 11:28 Codex Bezae inserts the words, "And there was much rejoicing; and when we were gathered together". The first person verb suggests that the author was present in Antioch at that time.
4. The Anti-Marcionite Prologue (2nd-4th century) says that Luke was "an Antiochian of Syria".
In conclusion, the author of Acts was a resident of Antioch and was probably Lucius of Cyrene (Acts 13:1). Paul mentions him in Rom 16:21 and uses the diminutive form of his name in Philemon 24. He was a witness of some of the events that he narrates beyond those covered by the 'we passages'. I believe that the identity Lucius (and that of Titus) would be more widely recognized if it were not for the misinformation found in the pseudonymous letters.