Objection 1. It would seem that Christ did not suffer in a suitable place. For Christ suffered according to His human nature, which was conceived in Nazareth and born in Bethlehem. Consequently it seems that He ought not to have suffered in Jerusalem, but in Nazareth or Bethlehem.
Objection 2. Further, the reality ought to correspond with the figure. But Christ's Passion was prefigured by the sacrifices of the Old Law, and these were offered up in the Temple. Therefore it seems that Christ ought to have suffered in the Temple, and not outside the city gate.
Objection 3. Further, the medicine should correspond with the disease. But Christ's Passion was the medicine against Adam's sin: and Adam was not buried in Jerusalem, but in Hebron; for it is written (Joshua 14:15): "The name of Hebron before was called Cariath-Arbe: Adam the greatest in the land of [Vulgate: 'among'] the Enacims was laid there."
On the contrary, It is written (Luke 13:33): "It cannot be that a prophet perish out of Jerusalem." Therefore it was fitting that He should die in Jerusalem.
I answer that, According to the author of De Qq. Vet. et Nov. Test., qu. lv, "the Saviour did everything in its proper place and season," because, as all things are in His hands, so are all places: and consequently, since Christ suffered at a suitable time, so did He in a suitable place.
Reply to Objection 1. Christ died most appropriately in Jerusalem. First of all, because Jerusalem was God's chosen place for the offering of sacrifices to Himself: and these figurative sacrifices foreshadowed Christ's Passion, which is a true sacrifice, according to Ephesians 5:2: "He hath delivered Himself for us, an oblation and a sacrifice to God for an odor of sweetness." Hence Bede says in a Homily (xxiii): "When the Passion drew nigh, our Lord willed to draw nigh to the place of the Passion"--that is to say, to Jerusalem--whither He came five days before the Pasch; just as, according to the legal precept, the Paschal lamb was led to the place of immolation five days before the Pasch, which is the tenth day of the moon.
Secondly, because the virtue of His Passion was to be spread over the whole world, He wished to suffer in the center of the habitable world--that is, in Jerusalem. Accordingly it is written (Psalm 73:12): "But God is our King before ages: He hath wrought salvation in the midst of the earth"--that is, in Jerusalem, which is called "the navel of the earth" [Cf. Jerome's comment on Ezekiel 5:5].
Thirdly, because it was specially in keeping with His humility: that, as He chose the most shameful manner of death, so likewise it was part of His humility that He did not refuse to suffer in so celebrated a place. Hence Pope Leo says (Serm. I in Epiph.): "He who had taken upon Himself the form of a servant chose Bethlehem for His nativity and Jerusalem for His Passion."
Fourthly, He willed to suffer in Jerusalem, where the chief priests dwelt, to show that the wickedness of His slayers arose from the chiefs of the Jewish people. Hence it is written (Acts 4:27): "There assembled together in this city against Thy holy child Jesus whom Thou hast anointed, Herod, and Pontius Pilate, with the Gentiles and the people of Israel."
Reply to Objection 2. For three reasons Christ suffered outside the gate, and not in the Temple nor in the city. First of all, that the truth might correspond with the figure. For the calf and the goat which were offered in most solemn sacrifice for expiation on behalf of the entire multitude were burnt outside the camp, as commanded in Leviticus 16:27. Hence it is written (Hebrews 13:27): "For the bodies of those beasts, whose blood is brought into the holies by the high-priest for sin, are burned without the camp. Wherefore Jesus also, that He might sanctify the people by His own blood, suffered without the gate."
Secondly, to set us the example of shunning worldly conversation. Accordingly the passage continues: "Let us go forth therefore to Him without the camp, bearing His reproach."
Thirdly, as Chrysostom says in a sermon on the Passion (Hom. i De Cruce et Latrone): "The Lord was not willing to suffer under a roof, nor in the Jewish Temple, lest the Jews might take away the saving sacrifice, and lest you might think He was offered for that people only. Consequently, it was beyond the city and outside the walls, that you may learn it was a universal sacrifice, an oblation for the whole world, a cleansing for all."
Reply to Objection 3. According to Jerome, in his commentary on Matthew 27:33, "someone explained 'the place of Calvary' as being the place where Adam was buried; and that it was so called because the skull of the first man was buried there. A pleasing interpretation indeed, and one suited to catch the ear of the people, but, still, not the true one. For the spots where the condemned are beheaded are outside the city and beyond the gates, deriving thence the name of Calvary--that is, of the beheaded. Jesus, accordingly, was crucified there, that the standards of martyrdom might be uplifted over what was formerly the place of the condemned. But Adam was buried close by Hebron and Arbe, as we read in the book of Jesus Ben Nave." But Jesus was to be crucified in the common spot of the condemned rather than beside Adam's sepulchre, to make it manifest that Christ's cross was the remedy, not only for Adam's personal sin, but also for the sin of the entire world.
Source: Summa Theologica (New Advent)