Star Trek Online has released a timeline summary that shows where the upcoming MMORPG will be set within the Star Trek Universe and canon. It also offers a simple way to see where the new 2.0 Universe created in Abrams' Star Trek is in relation to the Prime universe of the last 40 plus years. As far as the game itself, it is going to hop scotch over all of it by setting the game about 40 years after the end of Star Trek: Nemesis (or 20 years after Nero and Spock go back in time) to the year 2409 when the Federation is once again at war with the Klingon Empire.
The website also has a "Path to 2409" storyline that takes place starts about one year after destruction of Romulus in the Prime universe. In the Prime universe, the peace between Klingons and the Federation was partly out of necessity due to the threat of the Romulan Empire. With the Empire essentially destroyed, suddenly that necessity starts to crumble leading to events in the online game.