To find Valentino, Aizen had to return to Black Cloud Peak, to the Harmony Courtyard.
Valentino did not reside in Demon Mountain City, as the city was territory designated to Leo by the left faction.
The Harmony Courtyard and the surrounding vast area of Black Cloud Peak were territories allocated to Valentino, making him the one in charge there, a small leader appointed by the left faction.
The division of territories always involved disputes over resources.
After all, the western courtyard of the Heavenly Demon Clan wasn't solely dominated by the left faction. The rival right faction also held significant power, and besides these two, there were other minor factions as well, but we'll set those aside for now.
Within the Heavenly Demon Clan, fierce factional conflicts were common, and within each faction, there was even more intense internal competition.