Work your way to Don of NYC.
Another cool thing is that the game takes place in what looks to be realistic, 1930's New York City. At least certain neighborhoods. The game doesn't offer all that GTA San Andreas does in the way of flying planes and variety of missions. The Godfather is pretty straightforward, there's a lot of killing, shaking down business owners, and not a whole lot of anything else. Nevertheless, the game just does not get boring or old. You start off as a regular mob soldier, and eventually work your way up to the Don of the family. Then you work on taking over everything, eliminating the other families and becoming Don of NYC, which is basically where the game ends.
Whether or not you're a fan of the movie, the game is a must play for anyone who likes the genre.