As much as I love to spectate the world of NGE, I don't think I would want to visit. At any moment I could be crushed by angel or obliterated due to a character's decision to bring about the end of the world. If I could bang Asuka, Rei, or Misato, I might reconsider.
Banging those three would also do it for me.

But know that "You can (not) bang Asuka",
Asuka will bang you 
The Idea of going into a world where basically mankind has enslaved the gods angels and use them as weapons is very interesting, but if you are an non protagonist you gonna be in a bunker in fear and if you are a protagonist your chances of survival are very low : remember Asuka getting torn into pieces by Mass production models and Rei setting off a nuclear device. Not funny.
I wouldn't want to go into any Anime-verse with tentacles involved ... that is the redline for me.
Dragonball Z would be fun because I like Wilma and the whole Capsule Corporation thing, and Ben-to would be fun if only to meet the Female Cast.
Are we assuming that we are going to be in Anime form in this anime verse ? Cause some girls could become too ugly if not.