What time and place is Unwind by Neal Shusterman set in? How does the setting contribute to the story?

The place setting of the story is the United States.  The novel moves all across the United States as the author explores individual plot lines for the various characters.  For example, the Graveyard is in Arizona, and Lev and CyFi travel to Joplin.  
The time setting is a bit more difficult.  The reader is given a few specific dates at the beginning of a few chapters, but those dates reference events in the past. For example, there is an article at the beginning of one chapter that talks about a bunch of bodies being dug up from graves.  

In 2003 the authorities agreed to exhume around 30 bodies from a cemetery used by maternity hospital number 6.

The main events of the book take place sometime in the future, but it is a near future.  The best evidence that I can provide for a near future is when the Admiral is talking about "neurografting."  He explains that unwinding became a viable option once neurografting was made possible.  Currently, only certain organs and tissues can be donated, but neurografting makes it possible to use every piece of a donor's body.  

"I was right there in the room when they came up with the idea that a pregnancy could be terminated retroactively once a child reaches the age of reason," says the Admiral. "At first it was a joke — no one intended it to be taken seriously. But that same year the Nobel Prize went to a scientist who perfected neurografting — the technique that allows every part of a donor to be used in transplant."

Because neurografting is not current and available science, Unwind is taking place sometime in the future.