Yea I understand that it's not really as detailed a world as Shenmue's. From videos I've seen it's very action oriented, but how is the moment to moment gameplay? I read that there are things like the ability to take up jobs, do sidequests for people, etc. Is it an open city in Japan? Do you walk around in open world? Is there a form of mini-map?
The cities in the Yakuza games are open, but they're not particularly large. They're usually one district from a larger city (the main area being Kamurocho in Tokyo). Depending on the game there are usually multiple cities to explore (1 and 4 just had one, but 2,3 and 0 all have 2, and 5 has 5 different cities in it). So the areas aren't massive, but they're well populated, and more importantly, they become very familiar. There's something going on at every street corner, and as you play the games it'll start to feel like home. After playing the game for awhile you start to know all the nooks and crannies of the area and you can navigate the streets as easily as in your actual home town.
The games have lots of side quests that you can take for random people, and they tend to be very good. These are detailed side quests with a lot of story, some wackiness, and sometimes very interesting twists on the game play, not your typical open world bloat quests.
On top of that, the games have a load of side content to play (hostess clubs, batting cages, golf, karaoke, fighting tournaments, gambling, managing a club, and more). There's really a ridiculous amount of side content in the Yakuza games.
And one of the more interesting things they do as far as making you feel like you're living in real city is that you can go into all of the restaurants and bars and order anything on the menu. Eating food will heal you, and drinking will cause your character to get drunk (causing you to stumble around some with less steady controls, get into more fights, and be trickier to control while drunk). The game will even track every item you've ordered on the menus so you can try and eat every thing in the game.