My idea for a new Bioshock would be a sort of Greek mythology themed game, set it during the fall of Atlantis. Instead of plasmids you have magic (a bit boring, but it fits the theme better), the game could feature magi-tek weapons and environments and their use off magi-tek has pissed off the gods (as they believe the humans are getting too powerful) and they are destroying Atlantis, driving cultists to turn on the ordinary citizens in a futile attempt to appease the gods.
I believe with the ending to Infinite, there is so much untapped potential for games being a simmer experience but being different enough to keep them entertaining. I mean how many other games can have the kind of variety in discussions about a sequel that this topic already has.