Although we know for certain that a new BioShock game is in development, there's next to nothing else out there as to what the game will be about or where it will take place. Recently though, a brand new BioShock teaser website has been discovered, hinting that we could be getting some new information soon.
The site is named theresalwaysalighthouse.com, which is an obvious reference to the end of 2013's BioShock Infinite, where Booker and Elizabeth discover a realm of endless lighthouses, hinting towards the idea that there are endless worlds similar to Rapture and Columbia. All you'll find on the site though is a large star surrounded by smaller stars, an image that is named, "staytuned."
This could hint that the next BioShock game might bring us to a brand new dystopian world, instead of returning to the underwater city of Rapture or the airborne city Columbia. After all, "there's always a lighthouse", is a weird name for a teaser site if we're going back to a familiar lighthouse.
One can only hope that this means the upcoming BioShock will be revealed sooner than later. Reports suggest that the game is already well into development, and considering that BioShock Infinite was revealed in 2010, three years before its eventual 2013 release date, this could point to something happening very soon.
Source: Reddit