Puteoli

Where is "Puteoli" (Acts 28:13)?
Puteoli was next to the modern Italian city of Naples and 140 miles (225 kilometers) southeast of Rome. "Puteoli" literally means "little wells" in reference to the many hydrothermal wells that were in the city, which was well-known as a large port that could accommodate big ships. In fact, adjacent to Puteoli was Misenum, the Roman naval base that housed the largest naval fleet in the ancient world. Earthquakes have since sunk most of Puteoli under water.

How did they go "toward Rome" (Acts 28:14) from Puteoli?
On foot.

Why did they get off the ship so far - 140 miles -  from Rome?
The ship most likely wasn't going any farther, as Puteoli was the largest cargo port for Rome, especially for grain ships coming from Alexandria in north Africa.

Where is "Rhegium" (Acts 28:13)?
Rhegium is a port city at the extreme southern tip - right on the 'toe of the 'boot' - of Italy, across the narrow Strait of Messina from the island of Sicily. Rhegium, now called Reggio Calabria, is 210 miles (337 kilometers) south of Puteoli and 75 miles (120 kilometers) north of Syracuse.

Why did the ship carrying Paul circle "round" (Acts 28:13) to reach Rhegium from Syracuse, which is to its south?
The wind most likely was blowing from the west, so the ship first had to sail east and then diagonally against the wind to head north. When the wind then shifted and blew from the "south" (Acts 28:13), the ship was able to cover the 210 miles from Rhegium to Puteoli in just one "day" (Acts 28:13).

Where are "Appii Forum and Three Inns" (Acts 28:15)?
Three Inns and Appii Forum were 30 miles (48 kilometers) and 40 miles (64 kilometers), respectively, south of Rome. When the Christians in Rome "heard" (Acts 28:15) that Paul was headed their way from Puteoli, they walked for a couple of days and 30 to 40 miles south to greet him. "When Paul saw them, he thanked God and took courage" (Acts 28:15).