All of the stars rise in the East like the sun does, so saying they observed the Star of Bethlehem rising in the east I don't consider a clue to where they came from. Likewise them coming to Jerusalem from the East could just mean they entered through an Eastern gate. Now the location I'm going to suggest can be described as East of Jerusalem and Judea, but that's not necessarily the first or even primary geographical direction one is likely to use describing it's relationship to Judah.
Magi (translated Wise Men in the KJV) gets used as a proper name for a specific priesthood that is usually refereed to as Median in origin. But the word is only in that exact form once of all the times it's used in Matthew 2, and it's used elsewhere in the New Testament like in Acts 8 and 13 to refer to Samaritan and Jewish miracle workers, no one connects either of those individuals to Persia, Josephus also uses the word of certain Jews. The word Mage comes from the same term. In Ancient Greek texts it in time simply became their standard word for Magician in-spite of being non-Greek in origin. The following is copied form Wikipedia.
According to Robert Charles Zaehner, in other accounts, "we hear of Magi not only in Persia, Parthia, Bactria, Chorasmia, Aria, Media, and among the Sakas, but also in non-Iranian lands like Samaria, Ethiopia, and Egypt. Their influence was also widespread throughout Asia Minor. It is, therefore, quite likely that the sacerdotal caste of the Magi was distinct from the Median tribe of the same name."
Zaehner, Robert Charles (1961), The Dawn and Twilight of Zoroastrianism, New York: MacMillan, p. 163.Also in Jeremiah 39, Rabmag is clearly used of a Babylonian office.
Wikipedia is of course not always up to do date on how we now know the Median Magi were originally enemies of the Zoroastrian religion, they worshiped Mithra, they were not inclined toward Monotheism.
Isaiah 60:6 is often taken by scholars as being connected to the visit of the Magi because it refers to Gold and Incense/Frankincense, (in fact this verse is why they're often depicted riding Camels, Camels aren't mentioned in Matthew 2). The ultimate fulfillment is clearly about the Messianic Kingdom (either the Millennium or New Jerusalem or both) but it's believed that the visit of the Magi at Jesus Birth serves as a lesser near fulfillment, the Myrrh isn't in the final fulfillment because it represents His Death which is in the past by that point.
But when suggesting this connection it's often forgotten that specific nations are named there.
The multitude of camels shall cover thee, the dromedaries of Midian and Ephah; all they from Sheba shall come: they shall bring gold and incense; and they shall show forth the praises of Yahuah.All names linked to Arabia, but the big one is Sheba, indeed the visit of the Queen of Sheba to Solomon is also thought of as connected to this since Solomon is also a type of the Messianic Kingdom. Psalm 72 also further seems to back up Sheba playing this role. Jeremiah 6:20 is also an interesting reference.
Indeed history shows that the various nations of Ancient Yemen including the Sabaeans were the leading exporters of Frankincense and Myrrh, so to First Century readers that's possibly the first place they'd think of reading Matthew's account. And Gold we know could be found in this region because that's where Ophir was. The Ancient Kingdom of Saba continued to exist till 275 AD.
Tony Maalouf argues the Magi were from Arabia in "Were the Magi From Persia or Arabia?", Bibliotheca Sacra, 156 (October 1999), 423-42. The earliest report of the magi's place of origin is found in Justin Martyr, and he identifies them as Arabians (Dialogue With Trypho, 77). Clement of Rome, refers to Arabia as "the East", and associates the region with frankincense and myrrh, while addressing a context other than Matthew 2 (First Clement, 25).
Christianity is believed to have come to this region as early as 70-135 AD among Jews who fled the Roman destruction of Jerusalem.
From around 275-570 AD various calamities reshaped ancient Yemen among them were the conquests of the Himyar and the collapse of the Ma'rib Dam. That caused many Qahtanite/Joktanite Arabic tribes of Yemen to migrate North to Jordan and Syria. Among these were the Tanukhids from whom came the Christian Queen Mavia. And the Gassanids who formed a Christian Kingdom that controlled modern Jordan and much of modern Syria and the Golan Heights. And the Lahkmids who formed a Christian Kingdom in modern Iraq west of the Euphrates.
All in territory that was Biblically Ishmaelite, which probably explains why Mavia was mistakenly called an Ishmaelite in some Byzantine sources. Many of the Ishmaelites (mainly of Kedar/Qedar) began migrating south to the areas of Mecca and Medina after the fall of the Nabatean kingdom during the reign of Trajan.
All of this further backs up that the Queen of Sheba must have been a Queen in Arabia not Africa.
The Koran in Sura 2:62 refers to those who already in some way believed in "Allah" before Muhammad, and were distinct from the pagan polytheists. While most such references refer to only two groups, Jews and Christians, this one refers to three groups, those and the Sabeans. I don't think Himyarite Jews are what is meant, in fact I think most of Muhammad's references to Jews had primarily Himyar and Yathrib in mind, especially the Anti-Semitic verses, those were the Jews that he fought wars with. But I can't entirely rule them out either.
Jesus mentions the Queen of Sheba as an example of a Gentile who was saved. Many extra-Biblical traditions say that results in a conversion of her entire Kingdom. Maybe there is more truth to that then we thought.
The surviving Kings Lists of Sheba do not take us all the way back to Solomon's time. But only to 755 or 750 BC. This also seems to contradict certain traditions (mentioned in the Joktan link) that imply after king Phar'an the Kingdom was ruled only by Queens, (some of those look to me like they could be more feminine then our biases assume, but many are clearly masculine). At face value those traditions imply the Queen who visited Solomon was the last. But I have trouble seeing 60 Queens reigning in just the time from Reu to Solomon. So perhaps 755-750 BC marks when the Matriarchy was supplanted by a patriarchy.
According to one version of the Kings List, the King at the time Jesus was born was Yadail Darih II, who reigned from 10 BC-10 AD.
But since we've discussed the subject of Sheba's relationship to matriarchy. I feel like also pointing out that Matthew doesn't really tell us the gender of the Magi.
[Since I originally made this post the dates have been removed from the Wikipedia page for the Kings Lists of Sheba and Himyar]