When Does the Film "The Dark Knight Rises" (2012) Take Place?

"The Dark Knight Rises" is a superhero film written by Christopher Nolan with Jonathan Nolan and David S. Goyer [adapting "The Dark Knight" #1 (1986) by Frank Miller, as well as "No Man’s Land" and "Batman" #497 v1 (1993) by Doug Moench] and released July 20th, 2012. 

It takes place on an alternate timeline of the fictional DC Films Universe in the year: 

2016 AD 

We know this because, very early in the film, Gotham City's mayor speaks about the death of a character as "at the time of his death, 8 years ago" who fell in the climax of the previous film, "The Dark Knight" (2008), which takes place in July of 2008 AD. 

2008 + 8 = 2016. 

There is a time-jump at about two-thirds into the film referred to by two characters as "3 months". The bomb threat in the story is calculated to "5 months" from about this same point and the bomb is in danger of going off at the film's climax so there is a second 2 month time-jump. There's no definite answer as to whether or not the film moves into the new year. 

Additionally, the movie opens with a quick prologue that presumably takes place very soon after the conclusion of the previous film, "The Dark Knight" (2008). That story took place entirely in July of 2008 AD, so this very quick prologue must also be in mid to late-2008 AD. 

This is followed by a much longer prologue that is unplaceable but it's probably not long before the main action of the narrative starts so sometime during the 2010s AD. 

This StackExchange user examined the exact setting of the three movies called The Dark Knight trilogy. 

It is a chronologically late film in the DC Films timeline (the final chronological film to feature Bruce Wayne/Batman) and can be watched either at its timeline point, or after all the others.