Suppose I write:

{'elaDya' SepDaq vIghro'mey tIQ tu'lu'}.

This would mean: "there are ancient cats at the region of greece".

Now, suppose I write:

{'elaDya' DaqDaq vIghro'mey tIQ tu'lu'}

The way I understand it, this would mean "there are ancient cats at
the site/location of greece". And the only difference I "feel", is
that perhaps this sentence focuses more on the "location".

However, since I'm not a native english speaker, I wonder:

Meaning-wise, what's the actual difference between this and the first sentence ?

Do you, as native american speakers, "feel" any difference between
these two sentences ?

You're too focused on how the translation "feels" rather than what the Klingon actually says. Sometimes a single Klingon syntactic structure will "feel" differently with different semantics.

For example, you could say nuH pegh DaSov'a' Do you know the secret of the weapon? Do you know the weapon's secret? Both English versions a perfectly fine. But if you say 'elaDya' Sep DaSov'a', it sounds fine as Do you know the country of Greece? but it doesn't work at all as Do you know Greece's country? Identical syntax in Klingon doesn't mean entirely identical syntax in English translations.

In this case there is a difference because it is common to refer to a region by name ('elaDya' Sep) but not any old site by name ('elaDya' Daq). The first one will be interpreted as the region named Greece; the second one will be interpreted as a site in Greece (a Greece site), not as the place named Greece. 'elaDya' is a Sep, not a Daq, even if it is technically a Daq in a strict semantic sense.

-- 
SuStel
http://trimboli.name