Bioshock Infinite is the kind of game you want all of your friends to play even though it doesn't have multiplayer...
The Bad: Gamers who don't usually explore will miss out on a ton of the plot, shooting is pretty generic, a little bit on the easy side, too much hand-holding, no stealth elements, violence a little out of place, some side-characters are underdeveloped
Bioshock Infinite is the kind of game you want all of your friends to play even though it doesn't have multiplayer so you can discuss and debate about it. The ending was already (sort of) spoiled to me but nevertheless it still shocked me as everything unraveled. This game is of perfect length but at the same time you don't want it to end because the story and characters are very fantastic.
Bioshock Infinite has one of the most brilliant openings in gaming history, and while some games start off great but gradually get worse the story of Bioshock Infinite is constantly twisting and turning that you'll never get bored. Just a warning though: if you're the kind of person who only likes fast paced shooters where the goal is to shoot everything in sight, like Call of Duty, than you will not enjoy this game. A lot of the story won't make sense to you unless you walk around listening to audio diaries of different characters. so you need to be a patient gamer.
The core gameplay of this game kind of sucks. While it is promising at first, it quickly becomes "run away from your enemies before they shoot you" or shoot, possess, and electrocute everything in sight. It's not very difficult or punishing, and while this may bother some people for me this was good because it meant I could skim through these action moments to get to the story.
It's not fair to say that the combat is entirely bad however. Guns feel great to use (even though the controls for them are quite stiff), jumping off a sky-line to kill an enemy is awesome and you do get to destroy propaganda-spitting robotic George Washingtons (come on, doesn't that sound awesome?). I just wished that there was a little more to it, specifically in the stealth department (there is basically no way to sneak around your enemies). Maybe my hopes were just set too high by Dishonored's brilliant stealth sections.
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The true star of this game is Elizabeth, your companion. You play as Booker Dewitt, a man who is brought to Columbia (the flying city in which the game takes place) in 1912 to find and bring a girl back to America to pay off his gambling debts. The game tackles lots of mature issues such as racism and religion and the world is disturbingly racist yet completely beautiful at the same time. While Elizabeth is helpful in shooting sequences, the real reason you'll like her is because she is so kind and naive, yet still mature. She is flawed and perfect in her very own way at the same time. She feels real in the same way Clementine from The Walking Dead by Telltale felt real.
Booker is also a great character. His past is mysterious- even to him, and while he's done some really bad things in his life which haunt him, he isn't necessarily a bad guy. Unfortunately, it's a shame that only Booker, Elizabeth, and Comstock (the antagonist of the game who rules Columbia) are fully realized characters. There is a character I really liked in the game named Daisy Fitzroy (who leads the rebel group known as the Vox in Columbia) who is constantly described as being "no better than Comstock" which is never actually shown until one particular moment in the game which feels out of place and against her personality.
All in all, Bioshock Infinite is an amazing game. My nitpicks may seem numerous, but they are very minor compared to the game as a whole. You'd do yourself a disservice to not play this game because "it's shooting isn't the best" or because there is no multiplayer. This is the sort of game which will be discussed and analyzed for years to come.
(Review based on Xbox 360 version)
You can also read my second opinion of the game at: http://binarymessiah.wordpress.com/2013/06/09/bioshock-infinite/