Otherwise, you have them being located someplace in the west and then traveling east. Could they have been to the west in Rome, Alexandria, Spain....and then traveled to the east?
There isn't any evidence of that. In fact, the evidence is somewhat (although not certain) contrary in that it says they were "wise men from the east." Therefore, imo, their words indicate the meaning, "we saw his star (from our location) in the east."
Although, this interpretation isn't hard and fast. Perhaps they could have been easterners who were visiting in some land to the west of Israel so they could have traveled to the east in the direction of that star.
I like the other explanation better.