Location is not at issue, but belonging.
No, location is at issue in the first clause. The audience has no idea what the location is when Pan steps out onto the stage. He has to tell them. He says:
Τῆς Ἀττικῆς νομίζετ᾽ εἶναι τὸν τόπον
"Consider the location to be part of Attica -- Phyle . . . "
Phyle is in fact part of Attica. Pan doesn't say that the audience believes the location belongs to the Athenians, or the "Attics" -- the first clause says nothing about whom the location belongs to, just where it is. The Phylasians are "Attics" themselves. Actually, they are Athenians. All of the inhabitants of Attica, leaving aside metics and slaves, were citizens of Athens, and referred to as "Athenians," not "Attics." ἡ Ἀττική is a region, not a group of people.
Pan goes on to add that the nymphaeum belongs to the Phylasians. If δ᾽ draws a contrast here, it's between the general location and the nymphaeum itself--a very weak contrast that doesn't amount to anything more than a connective. If he had wanted to draw a contrast between what the audience thinks and what is in fact true, he would have to have been more explicit, and there's no point to such a contrast here. There's no point to be made here in insisting that Phyle belongs to the Phylasians, not the Athenians--otherwise, you would expect some explanation why it would be necessary to correct the audience's misperception.
νομίζω doesn't seem like the sort of word that you would use about something temporary like a stage.
Why not? "Consider the location to be part of Attica -- Phyle." Seems perfectly natural to me. What word would you use to tell the audience where to consider the scene to be set?
Menander sets his shrine to Pan next to a field, not on a cliffside.
The field is to the right, as the next verse establishes. The nymphaeum seems to be center stage.
This isn't a closely based on a real location.
What makes you think that? He's very specific about where the scene is set--Phyle, a village in Attica. Is there any reason why the nymphaeum is not well-known to the audience? Nymphaeums were typically natural grottoes or caves, at least before structures were built around them, which is Scribo's point. They would generally not be open to view. And while "open to view" is not impossible, in context it seems as if Pan is telling the audience to imagine the scene at a place that was well-known to them.