How about doing the game through the eyes of a redneck guy after his trailer park gets bulldozed for condos. He could decide to go after the developers, but discover that he has to work his way up through the powerful Vice City underground to get his shot at them.
Even though it sounds just like 4, you could be an immigrant who comes to America and does menial work before getting fed up and angling to be an underworld star. Unfortunately, a series of bad decisions and betrayals send it all spiraling down the toilet. Wait, actually that's Scarface.
You could be some hit man moving to VC to get away from the sordid life you once knew. Unfortunately, you find yourself in a "wrong place, wrong time" situation, and are indentured to various criminals as your dream of a quiet life slips away. All the while, your "work" attracts the attention of someone who wants revenge on you for your past, and plans to bring the wrath of heaven down on you in the finale.
Someone has slogged through the muck to emerge king of the town, and now sits on the throne of a crime empire, but you're not him, you're his daughter. When his top underlings band together and take him down, they fail to kill you. You lie low at first, doing jobs for low levl thugs and finally you get allies so you can start knocking them off and reclaiming your birthright. As you reap your revenge the conspirators start getting wise and try to correct their oversight.
Vice City has possibility for plenty of intriguing stories, so I can deal if they decide to go back, though my heart is set on a new San Andreas. It wouldn't matter who I played there, I just like the countryside.