I've been pondering this awhile now, still haven't come to any real conclusions though. I just can't get over the idea that the Post Apocalyptic Sandbox has some major differences from a fantasy sandbox. It occurs to me that the biggest differences boil down to three major things. 1) What Post Apocalyptic sub-genre will be used? 2) Where will it be set (on a post apocalyptic earth, or some other dimension/planet/realm)? 3) What caused the apocalypse?
The Post Apocalyptic sub-genre really breaks down into only two categories; Low Post Apocalyptic and High Post Apocalyptic. Low Post Apocalyptic settings tend to be more survival-oriented, take place relatively near the apocalypse, and don't feature a lot of mutants or weirdness. Road Warrior and zombiepocalypses are good examples of the Low Post Apocalyptic sub-genre. High Post Apocalyptic settings tend to feature more wackiness, often occur hundreds or thousands of years after the apocalypse, and have mutants, monsters, robots, (often) super science & sorcery, psychics, and all manner of bizarre and unusual things. Thundarr the Barbarian, Mutant Future and Gamma World are good examples of this Post Apocalyptic sub-genre. A lot of PA games tend to reflect a set sub-genre, though Post Apocalyptic Hero and Barbarians of the Aftermath have stuff for working with different sub-genres (regardless of what actual mechanics you use for your game).
Determining where your setting occurs is also a major factor. Choosing a post apocalyptic earth means you've already got a map to work with, though changes are inevitable. Choosing a different planet or dimension means you've got to create your own map entirely from scratch. Personally, I prefer to jack up the Earth and go from there.
The cause of the apocalypse is another major factor in creating a PA sandbox. It tells you what has been destroyed/damaged, and how. It also gives you hazards that are often geographical in nature. Nuclear war (a common apocalyptic event) means that there are going to have ruined areas and radiation pockets. Zombiepocalypses may see improvised walls, forts, etc. in addition to deliberately or accidentally destroyed areas (i.e. destroyed bridges, exploded gas stations, etc.). Alien invasions may introduce new and alien flora, structures, etc. Ecological disasters may see toxic regions, new flora (and fauna), and even some changes in things like coastlines. Other causes (say, for instance, a runaway comet hurtling between the Earth and the Moon...) may cause the very face of the land to change, mountains to rise up or sink down, earthquakes changing the shape of the land, seas rising or falling, etc. Of course maybe an ice age has occurred as a result of the apocalypse, or the ice caps melt, raising the sea level. And of course there is wastelandification, turning once verdant areas of plants into dry, desert-like regions. Even staying with using Earth as the basic setting doesn't mean the geography is going to stay the same.
On a minor note: The presence or absence of vehicles would be a factor in determining the scale of the sandbox. Characters using a vehicle with a long range (automobiles with a gas supply (or alternate), aircraft, ships, hover craft, etc.) will be able to cover more area than pedestrians and mounted characters.