Okay so its looking like Bioshock infinite is about a fantastical city set in the clouds, with a steampunk design ethic and what looks like a turn of the century American Exceptionalism ethic. So it seems like:
 
city + strong architectural theme + unlikely location + political philoshopy = a bioshock game
 
How about a moon base city designed by Frank Lloyd Wright, run by Dadaists?

"How about a moon base city designed by Frank Lloyd Wright, run by Dadaists? "

City: Pandora (it's trendy) 
Year: 2000
Architectural theme: Retro futuristic dome buildings
Location: Volcano
Philosophy: Communism

You got the pattern all wrong buddy. In Bioshock 4 you'll play as one of those robots we saw in the trailer. Takes place in Columbia. Bioshock 5 might be what you're describing.

" You got the pattern all wrong buddy. In Bioshock 4 you'll play as one of those robots we saw in the trailer. Takes place in Columbia. Bioshock 5 might be what you're describing. "

" @Rhode said:

" You got the pattern all wrong buddy. In Bioshock 4 you'll play as one of those robots we saw in the trailer. Takes place in Columbia. Bioshock 5 might be what you're describing. "

well the numbering is all sorts of messed up. Im pretty sure none of the remaining bioshock games will be numbered in the title. It just wouldnt make sense. "

Mars + Fascism + A Wild West setting inside a huge technodome = BioShock 4 
 

" Mars + Fascism + A Wild West setting inside a huge technodome = BioShock 4 
 

SPOILER WARNING: Click here to reveal hidden content.

During the final level, you break out and land on Earth to find it's in prehistoric times.

"

Thinking maybe an underground city in Italy would be a good setting.

" @HandsomeDead said:

" Mars + Fascism + A Wild West setting inside a huge technodome = BioShock 4 
 

SPOILER WARNING: Click here to reveal hidden content.

During the final level, you break out and land on Earth to find it's in prehistoric times.

"

Damn. That's actually a pretty good idea. I'd play it. "

maybe after Infinite, toning down the steampunk, and going for cyberpunk perfect worlds, Utopian environments, , maybe we'll see some of that in DE3. Mirrors Edge also had an interesting setting with its Utopian city but the game didn't explore that aspect enough. 
Or maybe aztec, mayan Eldorado style perfect cities and cultures to explore and see deteriorate.  
 
Something Sci-fi would really be cool. The Half-Life 2 series has done a good job illustrating a dystopian environment, maybe that could be a cool thing to flesh out further. 

actually someone could probably make a really sweet bioshock-type game based around the morlocks and eloi of The time machine, or a really sweet planet of the apes game with ape society and the surviving human psychic mutant guys.