Rapture is an underwater city located off the coast of Greenland and was built by Andrew Ryan to create a society free from religious and government interference. After a few short years, Rapture fell into anarchy, leading to the events of the original Bioshock. Booker and Elizabeth visit a version of Rapture (along with the Songbird) after Elizabeth opens a tear after the final battle on board Comstock's flagship. Elizabeth remarks that whatever universe there is, it's always a man and a lighthouse and a city, referring to Rapture underwater or Columbia in the sky.
It is notable that this probably takes place after the events of the original Bioshock, as the bottom of the stairs leading from the bathyspheres to the Gatherer's Garden is clear of rubble, the wrench is missing that Jack picks up in the original Bioshock and the Electro Bolt plasmid is missing from the Gatherer's Garden. It should also be noted that this may not be the version of Rapture that was actually seen in Bioshock. Some of the designs are different (such as the signs for the Vita-Chamber and the design of the upstairs by the Gatherer's Garden) and there is also a lock on the outer doors at the lighthouse. After Booker and Elizabeth step into the lighthouse, they are met by an ocean of countless lighthouses of Rapture, further adding weight to them not visiting the original because of the countless copies.
Of particular note, throughout the section that takes place in Rapture, Beyond the Sea plays in the background, further tying the two games together. In the distance, it is also notable that there is a Little Sister crying over the body of a Big Daddy in one of the glass walkways. None of the trash cans or bags of luggage are searchable and no other areas of Rapture past the first airlock seal are explorable. The posters and signs for Plasmids are still posted in this area, even though no weapons or plasmids can be found or picked up here.
On leaving Rapture in a bathysphere, Booker remarks about how the ridiculousness of a city underwater really sounds.
