Well I suggest getting Arkham Asylum first if you havent played that. It is really cheap now so make sure you get it (I liked it the same if not better than Arkham City)....
But as to your question, it depends on what type of game you like. Most people want to get Halo 4 right away because they want to start playing multiplayer. If you dont play MP, then I suggest getting Arkham City first and then getting Halo 4 when the price drops. Arkham City will keep you entertained for at least 40 hours of gameplay. Lots to do.
Arkham City is one of the best games I have ever played. That and Red Dead Redemption