To obtain the Missing: Greg lost and found quest in Dead Island 2, interact with the missing board at the Serling Hotel during/after The Search for Truth story quest. Afterwards, read the journal to learn that he was last seen in the parking garage behind LA 24 News. Make your way over to this parking garage then press the button on the elevator.
When the door opens, head inside and drop all the way down to the basement level. Once in the basement, head through the door. Work your way around the cars and the fire to reach a pile of pallets you can climb on top of to reach a higher level of the parking garage.
In this area, head through the doorway to reach a hall. At the end, you’ll find a circuit breaker box to place a circuit into. Do so then return to where Greg was. The gate will now be open. Take care of all the zombies waiting inside. Once you do, run after Greg then loot his corpse. As a reward, you’ll receive 2,000 XP and a Metal Bat.