In Mafia Town there's many fancy-looking doors leading to the center of the island and is also what i assume to be the source of the geyser keeping the mini island afloat. I'm able to get a quick peek inside by blasting through a few cannons that lead to the other side of the island, but other than that, two mafia members are always guarding the doors, telling you to go away. Can you get inside the cave? If so, is there anything worth going in for? I do not have any DLC.
The only way to get into the center of the island is through the cannons. It's more of a way to allow you to go to the other side of the island quickly than actually having anything.
None of the Acts or Time Rifts need you to go through the center of the island (Source)