Great story, but unfortunately its other short comings prevent it from being a great game overall.
You spend most of your time in the "overworld," the streets of Tokyo. The map layout is very similar to the Grand Theft Auto series with a couple of stores and locations you can enter, such as restaurants, "hostess" bars, shops, etc. The game is broken down into chapters and which require you to move back and forth between the same locations in order to advance the story. Most of the time it feels as if you are in "fetch" quests moving from one location to the next and then returning to a previous location. It's very linear, but it gets the job done in advancing the story. Side quests are given in the form of missions. I had a little gripe with the way they handled side missions because sometimes your left in the dark as to what to do or who you're chasing after. The menu screen doesn't do too well of a job in describing your missions for you. It can get mildly frustrating in completing all of the side missions if you don't know what to do.
While running through the streets of Tokyo, you will run into "random battles" with the people inhabiting the streets, most of the time they are just street thugs and generic Yakuza. The battle system plays much like a beat-em up, where all you really have to do is just beat the crap out of the enemies. There are special attacks here and there, but it really doesn't do much to help improve the bland combat. Sometimes the camera can be an issue and you'll find yourself missing punches and kicks – this can also be due to the poor collision detail in the game. You can also gain experience in this game to level up 3 characteristics: Body, Technique and Mind. As you level these up you gain new attacks and increase health.
Overall, the game has a great story – I still enjoyed the game. The minor problems however, add up to the point where the story alone cannot carry this game to greatness. Yakuza shows a lot of promise, but needs to polish it's gameplay mechanics. Hopefully the next Yakuza game fixes some of these issues. I'm looking forward to playing it.