I really enjoyed this one, but it does have some annoying flaws.
It's *technically* an open world game, but it might be the most linear one I've played. If anything, it's more of a "cinematic" open world game in the vein of The Getaway and The Getaway: Black Monday in that the world is open in name only really, and that the city is just an obvious backdrop for the story. Sure, you can drive around the city all you want before heading to wherever your mission is, but there isn't much of anything at all in the name of side missions. So with that in mind, the only reason to ever NOT go straight to your mission location is to drive around while listening to the in-game radio, or maybe to buy some new outfits.
The gameplay is generally alright, with one big problem. To get the topic of the problem out of the way, the problem is that it's only uses checkpoints for saving, and they're placed sporadically throughout each mission. That by itself is annoying, but it's made worse by the fact that Vito (the main character) isn't the most durable guy around, and later missions have him facing large mobs of err...mobsters. So yeah...get ready to replay some parts over and over and over and over because you had one enemy left out of ten and he got you.
To merge that complaint with some of the better mechanics, everybody in Mafia 2 is fairly "human" in their ability to take punishment, so you're on somewhat level ground there. Well, besides your allies, they're invincible, but the game balances that by making them absolutely useless in combat. The weapons all pack a believable punch, and the melee is simple but fun.
The cars feel nice and heavy and generally are fun to drive, although the faster cars in the last quarter of the game have a tendency to spin out when cornering. There is a nice variety of cars to find, and the more modern 50s cars really make it feel like times are/were changing. Not much else to say here...
The cops in the game were kind of annoying, which I imagine is the point to be fair, but I digress. To go back to my callback of The Getaway, in Mafia 2 you'll get in trouble with the local police for speeding, driving too erratically, getting in wrecks (along with being pursued for your criminal activity), as in The Getaway series. In my opinion they were a bit too attentive and a bit hard to get away from, with only one way to truly escape their heat at higher "wanted" levels (change your car and clothes). Sure, that's realistic but it's still annoying in a game where half of the things you do can lead to them being on your tail.
Missions are standard GTA-like missions. You know, tail this guy, go here and fight this warehouse full of enemies, etc etc.
Mafia II's atmosphere is top notch. It is set in two distinct eras, the mid 40s and the early 50s and it managed to make both feel unique, and believable. From war time radio news updates in the 40s, to the emergence of the rock n' roll fever of the 50s, the game used the radio to set the mood. As such, new songs were appearing, such as the debut of songs by artists like Little Richard in the last half of the game. Beyond the radio, cars were continuously updating, with new cars debuting throughout the game.
The writing was mostly hit and miss with more hit than miss. The dialogue is by far the strongest part of the writing and one of the game's biggest highlights. All of the characters come across as believable, with Vito and Joe being one of (if not THE) the best written friendships I've seen in a game yet. Rather than being the "forever supportive" friend trope that exists in most games, Vito would actually call Joe out on some of his stuff, nag him and generally see his faults. At the same time, he WOULD also be supportive, just not in the generic "good guy" way. Joe came across as a bit of a boisterous fool at times, but one who always wanted the best for himself and Vito, and he genuinely cared for all of his friends.
The main story and mission writing was the "miss" more often than not, once the game started its descent (or ascent, if you prefer) into the "epic" scale missions. Initially the game was somewhat grounded, with lots of world and character building and believable mission types. The last part of the game started slowly dropping established logic in the name of giving characters reasons to do things they otherwise wouldn't do, so the story could go on. Supposedly important characters were brought in and then quickly forgotten, then used later as a plot device and then never used again, smart characters did dumb things, that kind of thing.
It also has a tendency to beat you over the head with the "this is what you/Vito get for being a bad guy" moral stick towards the end of the game...which was pretty annoying. I really dislike when games assign you a role to play, and then punish you for playing that role, and unfortunately Mafia 2 really gets into it at times.
Overall I did enjoy the game a good bit, but if you haven't figured it out yet, I definitely feel that the first half of the game is a lot better than the second half. I've got no qualms with recommending it, just be aware that it does have some pretty annoying flaws.