This is not going to be a final review, just my first impressions from playing the game. I will have a more thorough review when I'm done with the game.
When I first opened it up, I was disappointed that the manual was just a folded sheet of paper. This is a trend I wish would go the way of the fanny pack. I'm sure I'll talk about this with a later rant. In the meantime, I'll get this show on the road.
As I started up the story mode, My jaw just about dropped when Bruce Wayne [spoilers deleted]. Walking through the entrance to Arkham City and meeting The Penguin for the first time was pretty awesome. I like how they portrayed him. When I stepped into the combat sequences, I found myself getting mixed up with some of the controls. For example, on Arkham Asylum, you'd double tap RT to use a quick batclaw in combat. In Arkham City, it's LT+Y. Threw me off quite a bit, and I still find myself getting mixed up every now and again. The additions to the takedown techniques and combat mechanics take a bit of getting used to in Arkham City, but hey, that's why there are roaming gangs on the streets! They exist to hone your skills!
When Rocksteady said that they were going to make Catwoman different from Batman, they weren't kidding. Her play style, while in a similar vein, is completely different. The jury's still out on whether or not I like it, but there's still time to decide.
I like the volume of side missions I've run across thus far. Between that and the Riddler challenges and trophies, something tells me that I'm going to be roaming Arkham City for quite a while.
Well, that's what I've got so far, Be sure to check back when I post my full review.