"The queen sleeps in a palace, not at a campground."

Translation: La reine dort dans un palais, pas dans un camping.

[LSadun]

Is the second dans really necessary?

[John.Orr]

Yes. It may not be necessary in english but it is in french

[MScottNataleonFB]

j'avais l'impression que << dans > sous-entend des endroits intérieurs alors qu << au > fait autant avec des endroits extérieurs [ des règles de base pour ainsi dire ]. J'aurais donc pensé que << non pas au camping > aurait bel et bien marché mais qui suis-je ? Héhé.
I was under the impression that "dans" implied but did not designate inside places whereas "au" did the same with outside places. I would have thought << non pas au camping > could've been just fine.

[kshamashas]

Why is ne not used?

[GraemeSarg]

Because there is no verb to bracket between "ne" and "pas".

[Sara24179]

Why not 'pas au camping'?

[John.Orr]

au = à le = at the. But the sentence says "a campground" so "le" isn't appropriate. But also in french they use the preposition "in" when you're in the place where you would pitch a tent. Actually even in English I would use "in" too in this sentence so the "at" here sounds weird to me. Maybe it's an american phrasing

[LSadun]

The phrasing is awkward in American English, too. The dissonance is that she sleeps in a tent (or doesn't because she's at the palace), but the hypothetical tent is pitched at a campground, so "at" sounds wrong after "sleeps", but "in" sounds wrong before "campground". Pick your poison.