Possible Clues:

• Irishman I caught climbing over hospital memorial
• Fallen monument?
• It's not cheap playing where there's nobody there
• The cap on? Whipped off, perhaps, here
• Church split by representation of pet on a memorial
• 'The Monument' is a church - not a pub!
• A broken cone and a crooked path for the dead
• Monument, exactly right one, put back in church
• Monument to honor soldiers
• Tomb in Greece, not a philosopher's