The sentence in question is “You can drop in to either library from 10am–5pm and make your notebook.” Should it be “to either library” or “at either library”? Thanks.
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There's no grammatical issue here. Either one is acceptable, and they mean the same thing.
While either may pass muster as "acceptable", "Drop in TO the library" is somewhat confusing, as it introduces the image of "dropping into" as in "through the roof/ceiling".
There may be some regions where the phrase "drop in to" is so common that there's no such confusion, but "Drop in AT the library" avoids the problem altogether, and that's what I'd choose.