There's the adessive case, which can be used to specify something is near a noun, but is there an opposite? Is there a case specifying a far distance from a noun? I'm including this case in my conlang whether there's a name for it or not, but it'd be nice to know what it's called.
If this List of cases on Wikipedia is complete, then there is no name (yet) for a case which expresses location far away from something.
Probably there is just no language that would express this by case (but by use of pre- or postpositions instead); location near by something or movement away from something is a more frequent thing to say.
You could abuse the movement cases (if so, most suitably I'd say ablative or elative), this would then correspond to what @bytebuster suggested, but I'm still not too happy with that, because those cases are used for motion and not for location, so it wouldn't reflect the meaning properly and would, as bytebuster said, possibly clash with other cases that express actual movement away from something.
If it's only about terminology, why don't you just think of your own case name? I think "Distantive", "Remotative" or "Procultative" would sound not too bad ;)
There's a nice table drawn in the Wikipedia's page for Finnish locative system. You may find it useful.
| System || Entering | Residing | Exiting | +--------++-----------------------+---------------+--------------------------+ | Inner || "into" illative | "in" inessive | "from in" elative | | Outer || "onto" allative | "on" adessive | "from at/on" ablative | | State || "into as" translative | "as" essive | "from being as" exessive |
Although it is not precisely what you need, your conlang may employ ablative or elative for this purpose (if you don't worry that "I'm away from home+ABL" would clash with "I'm leaving home+ABL").