In this question, it was determined that a PC visiting another plane can, in fact, be banished back to the Prime Material, since they will have the Extraplanar Subtype while traveling.
The text of that Extraplanar subtype, from the SRD:
Extraplanar Subtype
This subtype is applied to any creature when it is on a plane other than its native plane. A creature that travels the planes can gain or lose this subtype as it goes from plane to plane. Monster entries assume that encounters with creatures take place on the Material Plane, and every creature whose native plane is not the Material Plane has the extraplanar subtype (but would not have it when on its home plane). Every extraplanar creature in this book has a home plane mentioned in its description. Creatures not labeled as extraplanar are natives of the Material Plane, and they gain the extraplanar subtype if they leave the Material Plane. No creature has the extraplanar subtype when it is on a transitive plane, such as the Astral Plane, the Ethereal Plane, or the Plane of Shadow.
The Banishment spell doesn't say where they go, just:
A banishment spell is a more powerful version of the dismissal spell. It enables you to force extraplanar creatures out of your home plane. As many as 2 Hit Dice of creatures per caster level can be banished.
Dismissal says:
This spell forces an extraplanar creature back to its proper plane if it fails a Will save. If the spell is successful, the creature is instantly whisked away, but there is a 20% chance of actually sending the subject to a plane other than its own.
So this begs two questions.
- Does Banishment also carry the 20% chance to go somewhere random? (Banished from Plane of Air to… Plane of Fire!)
- If the PC is sent back to the Prime Material successfully, Do they "automagically" go to their own world? To their own continent? To a anywhere they have ever even known?
In other words, if some meddlesome PCs from Forgotten Realms (say, as an example) muck about in the planes, could they get banished to somewhere like Kara-Tur, or Maztica? Or could they even find themselves further out from "home;" stuck in the world of Dark Sun or Greyhawk?
Best Answer
Yes -- banishment says it is "a more powerful version of dismissal", and it doesn't override the 20% chance, so that is in fact how it works.
Given that your question is tagged "pathfinder", by the Rules As Written there is no way that the PCs could wind up in Maztica or Dark Sun or Greyhawk (as these are all D&D settings).
A very literal-minded DM might argue that, since no destination within the Material Plane is specified, the PCs arrive at an entirely randomly chosen location, which is overwhelmingly likely to mean they show up in airless deep space, far from any sun. Let's hope they have a silent greater teleport spell ready!
A less literal-minded DM might treat the dismissal effect as though the PCs had cast plane shift -- they'd appear "5 to 500 miles (5d%)" from the place they left the Material Plane.
The Pathfinder Wiki has some words about the Pathfinder settings that officially exist on the Prime Material Plane. If you're determined that the player characters arrive on the surface of a human-livable planet, but you'd prefer that it be a randomly selected planet, your choices include Golarion, Earth, Androffa, Kasath, and, er, Carcosa.
Of course, this is your cosmology; if you'd like to rule that multiple D&D settings exist in your version of Pathfinder's Material Plane, that is your prerogative.