For some fluff, check out the Pathfinder Tales novel, The Redemption Engine. I think it's the first one where the main character travels to a number of planes.
The cosmology of Golarion isn't tremendously different from the 3.X D&D cosmology of the Great Wheel. There are planes associated with each alignment that souls are naturally drawn to after death. The goddess Pharisma is in charge of making sure the souls make it to the right afterlife. Asmodeus is not just the king of the devils, but a fully-fledged god. The slaad have been replaced by the proteans.
There are three supplements, The Book of the Damned vol. I, II, and III that cover the denizens of the lower planes in pretty good detail. Another supplement, Chronicles of the Righteous cover the good-aligned outsiders. Nothing for the elemental planes or for the inevitables or the proteans beyond their entries in the various bestiaries so far, though.
So, while there isn't a single book by Paizo describing the planes, there are a number of supplements covering at least some of them. But since it is so similar to the 3.X cosmology, you could use a lot of the fluff from the Manual of the Planes and Planar Handbook and incorporate it into your campaign without much difficulty.