Astral Projection seems like a pretty good way to explore the world and the planes (setting aside any questions of protecting my wizard's original body and the silvery cord).
However, the plane-hopping part's annoyingly vague, consisting entirely of:
Since the Astral Plane touches upon other planes, you can travel astrally to any of these other planes as you will. To enter one, you leave the Astral Plane, forming a new physical body (and equipment) on the plane of existence you have chosen to enter.
So:
Part 1: where on the target plane do you appear? Is it like Plane Shift, where you appear 5d% miles from your target; like Gate, where you appear exactly where you want; or "GM Fiat", where you appear somewhere on the plane, but that's all you get?
Part 2: can you return to the astral plane for more sightseeing as part of the original casting of Astral Projection, or do you need to do something to get back there (plane shift, etc.)? The spell seems to imply that you can just pop back to the astral plane and continue on your merry way, but isn't quite explicit on that point.
Best Answer
The mechanics/setting-agnostic version
The Astral Plane is “coterminous” with other planes, since it is the space between them. That is, where one plane ends, the Astral begins (barring cases where two planes are in immediate contact with one another, which is the case in a number of places). So when you leave the Astral Plane, you are just stepping across the boundary from the Astral side to the side that’s whatever plane you’re visiting. If you can recognize and find the portion of the Astral that touches upon the part of whatever other plane you’re looking for, you can step out at exactly that point, every time, if you like. But you’ve got to find that spot in the boundary.
How you find that spot isn’t precisely spelled out, but ultimately the idea of astral projection is that it’s a whole lot more like regular adventuring than a teleportation spell like plane shift. Finding the right spot is a question of knowledge, skills, and so on. One expects that Knowledge (planes) and Survival would likely be involved, for example. Divinations are quite plausible. Etc. It is ultimately the same as trying to find your way to the other side of a mountain range or whatever, just in the weird Astral Plane.
As for your second question, yes, astral projection indicates that when you reach another plane, you are still projecting, still under the influence of the spell’s magic, and can continue to return to the Astral by just passing through the boundary again. Note that only certain geographic portions of other planes are actually adjacent to the Astral Plane: for instance, in D&D’s Great Wheel (which the d20 System that Pathfinder is based on roughly inherits without naming it as such), the first layer of an Outer Plane is Astral-adjacent but the other layers are not. You can presumably steer your projected body into these further layers, stretching the silver cord straight across the first layer, but you would have to return to the first layer to be able to re-enter the Astral.
Golarion?
I am not very familiar with the Golarion setting, but a quick look at the Wiki suggests that in this setting, the elemental planes wrap around the Material and Shadow, with the Plane of Fire being the outermost shell and the only one of the lot to touch the Astral. If this is the case, you wouldn’t be able to cast astral projection from the Material Plane at all, since the Material wouldn’t be adjacent to the Astral. That’s a problem, of course, since astral projection references the Material several times—but honestly that was always dumb, we should read “Material” in each case as “wherever you were when you cast the spell, where your original body is still sitting in suspended animation.” Of the other planes, only Hell and the Abyss seem to have layers, so I guess you can astral projection into any location in the Outer Sphere aside from those other layers of Hell and the Abyss if you can find the right spot in the Astral to step out from.