Final answer:
Horatio and Hamlet meet at the castle after midnight in Act 1 scene 2 to discuss the ghost.
Step-by-step explanation:
The correct answer is Option 1: At the castle, after midnight, to discuss the ghost. In Act 1, scene 2 of Hamlet, Horatio and Hamlet meet at the castle after midnight to discuss the appearance of the ghost of Hamlet's father. This meeting is significant as it sets the stage for the central conflict of the play and introduces the theme of revenge. Horatio's presence provides a witness to the ghost's appearance, confirming its existence to Hamlet.