[Extra love]

Where specifically does the most significant production of ATP occur in prokaryotic and eukaryotic cells?

[Arkcon]

That really depends on whether you're talking about a eukaryotic cell or a prokaryotic cell, (hint: what is the connection between the two, as per a well known hypothesis?), and how "specific" a place you mean when you say "specific".  Text book or class notes will give you the answer you can use best on an exam, but for general info, do you mean a cellular structure, a position on a cell, a type of macromolecule, any one of those could be the answer, again, a different one for eukaryotes and prokaryotes.  You do know exactly how the final chemical energy is transfered to ATP, right, (Hint: some sort of gradient, correct?)