TrekMovie is reporting that when principle photography for Star Trek 3 starts around mid-February 2015, most of the filming will take place in Vancouver, Canada. The previous Star Trek films were mostly shot in the Los Angeles area but the change to "Hollywood North" is mostly driven by tax incentives. It doesn't hurt that the area has been used for TV and film for decades now and so has all the resources they will need to shoot the film regardless of whatever "alien" location that might be needed for the story plot.
Filming there will also include rebuilding the Enterprise sets all over again as a rebuild. The decision was made in part because the Enterprise set was repurposed into the Vengeance set and so between restoring it and shipping it, just became more cost effective to rebuild. It has also been indicated that some filming will take place in Seoul, Korea. As usual though, no details on the story plot or what the locations will be used for.