Where did Saint Gabriel the Archangel live?

Catholic AnswerSaint Gabriel, being an angel, lives in heaven. Being entirely spirit and not having a body, he does not live in a "where" so much as a state. Angels are messengers and guardians of humans, the Word "angel" is his nature, archangels are named in The Bible, and bear important messages for the whole human race:

from Modern Catholic Dictionary by John A. Hardon, S.J. Doubleday & Co., Inc. Garden City, NY 1980

Angel. A pure, created spirit, called angel because some angels are sent by God as messengers to humans. An angel is a pure spirit because he has no body and does not depend for his existence or activity on matter. The Bible tells us that the angels constitute a vast multitude, beyond human reckoning. They differ in perfection of nature and grace. Each is an individual person. According to Christian tradition, they form three major categories in descending order. The Word "angel" is commonly applied only to those who remain faithful to God, although the devils are also angels by nature. Moreover, "angel" is the special name for the choir of angelic spirits, from whom guardian angels are sent to minister to human needs. The existence of angels has been twice defined by the church: at the Fourth Lateran Council (Denzinger 800) and the First Vatican Council (Denzinger 3002). (Etym. Latin angelus, an angel; Greek angelos, messenger).

Gabriel. One of the seven archangels, used on a number of occasions by God as a messenger (Deuteronomy 8:15-27). He appeared to Daniel and explained a vision to him about future events, telling him, "You are a man specially chosen" (Deuteronomy 9:20-27). In the New Testament he appeared to Zechariah to announce that Elizabeth, his wife, would bear a son and he must name the child John (Luke 1:11-20). Likewise, it was Gabriel who appeared to Mary and told her that would conceive and bear a Son whom she must name Jesus (Luke 1:26-38).