He hung around the entrance all day, hoping for a chance to speak to the director.
The underlined phrase means

The correct answer is Option C (both, (1) and (2)).

Key Points:
• Meanings and nuances of the phrasal verb 'hang around'.
• The phrasal verb 'hang around' (or 'hang round') standardly means to spend time in a place waiting or with no clear purpose, i.e., to loiter as well as to wait around.
• Since both 'loiter' (staying aimlessly or lingering) and 'wait' (anticipating someone's arrival) capture the contextual and literal meaning, Option (3) is the intended comprehensive answer.
• Key Takeaway: 'Hang around' means both to loiter and to wait around a place.