Falcar is located in the city of Cheydinhal in The Elder Scrolls IV: Oblivion. Specifically, he can be found at the Cheydinhal Mages Guild Hall, where he sleeps in his locked chambers in the basement before the Cheydinhal Recommendation quest

. During this quest, you interact with him in the Mages Guild to retrieve a ring and later search his quarters for a recommendation letter

. After the quest reveals his secret practice of necromancy, Falcar flees Cheydinhal and joins the Necromancers Cult. You encounter him again later at Silorn, a location south of Cyrodiil, where he is with his necromancer allies during the Ambush quest

. In summary:

• Before the Recommendation quest: Falcar is in the Cheydinhal Mages Guild basement chambers

• After the secret is revealed: He flees and is found at Silorn during the Ambush quest

This covers where Falcar can be found throughout the relevant parts of the game.