By "Green Card" I assume you mean a US Residence Permit. That serves no purpose outside the USA, leave it in your hotel.
The only valid ID is your passport. If you need to show ID, it will be your passport. I would keep that in an inside pocket, in case you need it. If you think you won't need to show ID, leave it in your hotel room.
You also need to bring enough cash for the day, not all your cash, leave the rest in your room. Plus a card (debit or credit) to get more cash or pay big bills (restaurants). Again, if you have multiple cards leave the rest in your hotel, then if the worst happens, you still have some cash and cards.