I'd pick up Arkham Asylum before getting Arkham city if I were you. I'm not sure if you're a PC gamer or not, but they've been having great deals on both games over the last few days. As far as Borderlands 2 goes, if you've played the first one, you know what you're getting into with the second one. It's much more fun if you play with people you know though. Might be a good idea to pick up the season pass if you plan on getting all the DLC with it too.
If it was my choice, i'd go with Borderlands 2, since you'll probably get more play time out of it.