Well personally, for my character, he would be more leaning towards the island. Maybe he even partied the other night at that island so he would have some kind of memory of it? Because honestly he knows nothing about anywhere about that place besides what he's heard and where he's been, which is around the beach and hotel. Having a safe and secure base would be pretty optimal, and he wouldn't mind putting in the work to make supply runs to places that might have more supplies. The only issue would be that they'd need a boat of some kind to transfer the supplies to the island. And, once supplies dry up, they might need to move anyways. 

Now I would also be more than happy to possibly explore and find some less mainstream options, because in the back of his mind Cole would be like "Okay, let's go where everyone is not going to go. The zombies are probably going where the people are." A map would be quite helpful for all that, and who knows, maybe he'll be convinced otherwise.

There's also the problem of how are we going to get out of the control room with all the zombies waiting for all of us on the other side? I suggested maybe setting off an alarm, like a fire alarm, to distract them, or maybe there's a ventilation shaft. Because, as Cole noticed, these things for the most part can get distracted.