Clue: One possible choice for Hamlet appearing before jolly or unknown island town (9)
Answer: TOBERMORY
Explanation: Definition: island town
A charade of TO BE (or not to be, 'one possible choice for Hamlet') plus RM (Royal Marine, 'jolly') *plus 'or' *plus Y (mathematical 'unknown'). On the Island of Mull in the Inner Hebrides.