Fellow duders, I might be reading too much into this, but I recently watched a movie that reminded me a lot about Bioshock Infinite. Granted, I watched this movie after I played the game and I found it by chance when I searched for movies about time travel as a theme.
Anyway, there's a movie called Somewhere In Time, where man named Richard goes back in time to 1912. Same year as Bioshock Infinite takes place. Probably a coincidence I thought, but I had to watch the movie just to be sure.
So why does he go back in time? Well, the movie starts in 1980, where an old women give him a pocket watch and says "Come back to me". Apparently she's waited a long time to meet him. Sort of reminded me about Comstock House where you met Elisabeth as an old woman and she gives you the instructions on how to control Songbird.
The woman he's going back to, is a 25-something brunette actress named Elise. She's guarded by her manager, an older man that has warned her about "the one". She even tells Richard that he could see things before they happened, about her career and her life. This is of course the same women he meet in 1980.
The way Richard goes back in time also kind of reminded me how Booker constructed memories. He goes back in time by self-hypnosis, basically he convinces himself he's back in 1912. He forces out the memories from 1980 and imagine 1912 instead. This has consequences of course, similiar to the nose bleeding in the game when memories come back. In the end of the movie, he forgot to take out a coin from 1979 in his pocket and when he accidently pulls it out, his memories collide and pulls him back to 1980.
Does this sound a lot like Ken Levine could have taken some inspiration from this movie? I haven't seen it mentioned anywhere else. There's even a lighthouse in the movie that plays a part, but not as central as in Bioshock.