The game is set in 2008, the year the game was released. It is specifically between July and October:

In The Ballad of Gay Tony, whose timeline intersects the original GTA IV frequently, Gay Tony mentions in I Luv LC that "the banks" had been bailed out which was made official on October 3, 2008.

A Weazel News segment on the radio says that Paper Trail and Entourage were about one month apart.

Another Weazel News radio cast says that a month after the Platypus captain's body was found, shipmate Dave Bosoy was also found dead - Dave was found around the same time as Undress to Kill.

Ernesto Lopez mentions to Luis Lopez that his children are in school.

The entire plot also likely happens in less than three months - a celebrity named Cloe Parker has a three-month-old child, and in tabloid tradition there would have been extensive coverage of her pregnancy.

The real-life New York City begins to snow around mid November, and it never snows in the game.

It's never revealed whether John Hunter or Michael Graves was elected governor, which would have occurred in early November.