Almost Perfect.
The whole story is based around Booker DeWitt and a girl named Elizabeth which he is supposed to retrieve in order to "wipe away the debt". This leads you into a gradually darkening world where not everything is as it seems. Which gives me one of my favorite gaming quotes ever "Lives, Lived, Will Live it is all a matter of perspective" (you will understand if you play the game).
Unlike the previous Bioshock's you can only carry two weapons at a time, while at the same time their are several new weapons available. This means you are constantly trying to scrounge for the weapon you need, which brings up a flaw with Elizabeth. Yes she keeps you decently stocked on ammo and salts but she can't keep an extra weapon or two for you which would have been a tremendous help in some of the more drawn out battles. At least you still have all of your plasmids, or Vigors as they are known in this game, which is a saving grace but most of the stronger enemies are immune to one or more of these Vigors leading you to constantly trying to remember the prearranged shortcut keys (no customization here) or using the clearly console designed Vigor wheel. Another major flaw in this game is its linearity in both story and map design. Sure you can backtrack to a previous point but only to a certain extent and some side areas are locked down after your visit meaning you miss some side objectives. Also in an age where even COD is going to multiple endings Bioshock Infinite still only has one ending despite giving you a few points of apparent decision making. There are plans for DLC's but I wonder how well these well play into such a linear storyline, only time will tell.
There are some extremely good points about the game that vastly out way the negatives. The introduction of sky-lines takes both travel and combat to a whole new dimensions and with enemies that traverse the lines as well you constantly have to watch your back or risk being flanked. The enemies while frustrating at first all have a particular trick to defeating them and on the highest difficulty this game provides a decent challenge to even the most skilled of FPS gamers. The departure from Rapture also opens up an entirely unknown world to players of previous games meaning that although map design is quite linear it is very intriguing with enough side missions to keep you busy for more than a few hours. Music is also very mood appropriate with everything from upbeat turn of the century quartets to somber dirges when needed.
All in all this is a great game the story, graphics, and gameplay means that this game is worthy of the Bioshock name. However it offers little in the way of innovation and takes a few steps back on weapons leading me to question just what is in store for the Bioshock series.