I bought this for my nephew, and he absolute loved it. From what I saw of the game it the graphics are amazing. The storyline is excellent (being a long time Batman fan that is the thing I am most qualified to comment on), and the game play is addictive he could not put it down.
After some time with this game now I have found myself wholly impressed. I was a huge fan of the first of Rocksteady's Batman games (Arkham Asylum) having played it from beginning to end on numerous occasions. Batman Arkham City takes everything that was so great about Asylum and expands upon it immeasurably, then adds a load of new stuff for you enjoyment! Firstly, after a stunning opening sequence the game drops you straight into the action in the heart of a city overrun with criminal masterminds, mindless thugs and a good smattering of doctors, security and police personel who are trying to help bring pockets of order to what is essentially a city in a state of riot. The beauty of being dropped straight into the action is that you immediately get the impact of the scale of this game - the environment is huge and explorable in a variety of ways. Straight off the bat (sorry) you can run, jump, glide, grappel, slide throughout the city. More and more of Batman's gadgets become available throughout the game allowing for access to the tiniest corners or furthest reaches of Arkham but you are free to explore a vast amount of the city and a good deal of gadgets from minute 1.
For me, the most notable improvements have to be the fact that the larger environment has allowed for side quests to be included. In the first you pretty much went from A to B occasionally stopping to collect riddler trophies. Yes it was fun, but also gave you a fairly linear story within Arkham Asylum. In Arkham city, you have the run of the city, you ARE Batman and whilst there is a strong narrative throughout - you can feel free to help this person, destroy that danger or discover those secrets without ever feeling like you're deviating from what the game wants you to do.
Riddler challenges have been massively improved too! No longer are they all hidden behind destroyable walls and in hard to reach places that you need a specific gadget for. Now they actually challenge you to think logically, or laterally or test your memoery, dexterity etc. They all actually feel like challenges for Batman from the Riddler! Also, the ability to record riddler challenges onto your own map if you can't reach them yet, or don't have time to collect just now etc. is an excellent and welcome addition.
One of the only criticisms I have read about this game is the inclusion of SO many villains that some are reduced to cameo performances rather than fleshed out stories - again, for me this plays into the story world beautifully. Imagine the world of Batman, played to such a scale as a whole city to explore yet only brushing shoulders with one or two villains!??! I feel that the scale demands the number of villains - and again, the games variety means thast some will be playing the role of main antagonist, some will be unlikely ally, some will be chance encounter. Stands to reason really!
Final thought is simply this. This is an outstanding game with many jaw dropping moments! Just remember to download the free Catwoman as a playable character element BEFORE you start playing the main game! It actually slightly changes the game right from the outset, but all in good ways!