Objection 1. It would seem that adoration does not require a definite place. It is written (John 4:21): "The hour cometh, when you shall neither on this mountain, nor in Jerusalem, adore the Father"; and the same reason seems to apply to other places. Therefore a definite place is not necessary for adoration.
Objection 2. Further, exterior adoration is directed to interior adoration.
But interior adoration is shown to God as existing everywhere. Therefore exterior adoration does not require a definite place.
Objection 3. Further, the same God is adored in the New as in the Old Testament. Now in the Old Testament they adored towards the west, because the door of the Tabernacle looked to the east (Exodus 26:18 seqq.). Therefore for the same reason we ought now to adore towards the west, if any definite place be requisite for adoration.
On the contrary, It is written (Isaiah 56:7): "My house shall be called the house of prayer," which words are also quoted (John 2:16).
I answer that, As stated above (Article 2), the chief part of adoration is the internal devotion of the mind, while the secondary part is something external pertaining to bodily signs. Now the mind internally apprehends God as not comprised in a place; while bodily signs must of necessity be in some definite place and position. Hence a definite place is required for adoration, not chiefly, as though it were essential thereto, but by reason of a certain fittingness, like other bodily signs.
Reply to Objection 1. By these words our Lord foretold the cessation of adoration, both according to the rite of the Jews who adored in Jerusalem, and according to the rite of the Samaritans who adored on Mount Garizim. For both these rites ceased with the advent of the spiritual truth of the Gospel, according to which "a sacrifice is offered to God in every place," as stated in Malachi 1:11.
Reply to Objection 2. A definite place is chosen for adoration, not on account of God Who is adored, as though He were enclosed in a place, but on account of the adorers; and this for three reasons. First, because the place is consecrated, so that those who pray there conceive a greater devotion and are more likely to be heard, as may be seen in the prayer of Solomon (1 Kings 8). Secondly, on account of the sacred mysteries and other signs of holiness contained therein. Thirdly, on account of the concourse of many adorers, by reason of which their prayer is more likely to be heard, according to Matthew 18:20, "Where there are two or three gathered together in My name, there am I in the midst of them."
Reply to Objection 3. There is a certain fittingness in adoring towards the east. First, because the Divine majesty is indicated in the movement of the heavens which is from the east. Secondly, because Paradise was situated in the east according to the Septuagint version of Genesis 2:8, and so we signify our desire to return to Paradise. Thirdly, on account of Christ Who is "the light of the world" [John 8:12; 9:5, and is called "the Orient" (Zechariah 6:12). Who mounteth above the heaven of heavens to the east (Psalm 67:34), and is expected to come from the east, according to Matthew 24:27, "As lightning cometh out of the east, and appeareth even into the west; so shall also the coming of the Son of Man be."
Source: Summa Theologica (New Advent)