Philip, the evangelist (Acts 21.8), was among those of the Jerusalem church who were “scattered throughout the regions of Judea and Samaria...preaching the word”(Acts 8.1, 4). Philip chose, of these two regions, Samaria for his mission field.
Samaria was both a region (1 Kgs. 13.32; Acts 1.8; Jn. 4.3-5), as well as a city (1 Kgs. 16.24), about 30 miles north of Jerusalem. However, the city
“had been destroyed by Hyrcanus, so completely as to leave no vestige of it remaining” (Barnes, Acts, 138).
Herod rebuilt the city, renaming it Sebaste, “so called...in honor of Augustus” (The Expositor's Greek Testament, 211).
Therefore, when the text says, “Philip went down to the city of Samaria,” it most likely refers to the main city of Samaria (the region); or even simply, “a prominent city of Samaria” (Jackson, Acts, 88); not to any city then named Samaria.
It is possible Sebaste is intended, or perhaps another city of Samaria, including Sychar, where Jesus had met the Samaritan woman and her neighbors (Jn. 4.5 — note: “a city of Samaria,” as rendered here without the definite article, could also be an accurate translation of Acts 8.5).
The text also observes that Philip “went down” to Samaria. This refers, not to direction, but to elevation. While Jerusalem, the city from which he journeyed, was located south of Samaria, requiring him to travel northward, it was higher in elevation (some 2500 feet above sea level), requiring him, literally, to go “down” to arrive in the region.