We learn the specific date of the story after a glimpse into Teddy's diary. The most interesting element of the setting is the fact that it takes place on board a cruise ship. We don't know exactly where the characters are – somewhere on the Atlantic between Europe and America. What we do know is that they're moving, traveling from one location to another. All we see is a small slice of a much larger journey that everyone is passively taking together.
It might be a bit of a stretch, but it's tempting to think of the setting as a large-scale metaphor for the idea of reincarnation. As Teddy explains, each physical life that one lives is a small step in the longer journey of the spirit. Like it or not, everyone is on this ship together and moving forward in one direction.
Another element of setting to consider is the image of the empty pool on top of the ocean. Check out "Symbols, Imagery, Allegory" for a discussion of "emptying out" in "Teddy." If you're interested in the connections between "Teddy" and "A Perfect Day for Bananafish," you should know that the latter takes place on a beach, while Teddy is out in the middle of the ocean. Something to think about, at any rate.