Hey there! Thanks!
Joy can be found right outside your apartment. As for the ant maze, the exit is at the very top. Also, for the locked doors in the Industrial District, it depends on which doors. There's one building that's next to the factory that is inaccessible. I sometimes put certain locked doors in areas I might return to give a side quest. A.V.A doors are only unlocked by meeting a certain character in New Game Plus. Any other locked doors should have a quest connected to it.