What is the difference between at a hotel and in a hotel? The NYTimes seems to be using both of them. I looked up the ngram on google and it seems in a hotel is used more often than at a hotel, which is kind of surprising to me.
I think in a hotel is more specific. It means being inside the hotel. When you use at the hotel it can be both inside our outside.
In a comment responding to the original post, Eduardo advises the poster to add a verb in front of the phrases "at a hotel" and "in a hotel" to more nearly balanced idea of which phrase is more common.
A further complication in any such assessment involves the presence or absence of a noun following "hotel" in the phrase. I ran Ngram searches for three pairs of verbs + the phrase "in/at a hotel": "met at a hotel" vs. "met in a hotel"; "stayed at a hotel" vs. "stayed in a hotel"; and "stopped at a hotel" vs. "stopped in a hotel." In all three instances the "in" phrase was likelier than the "at" phrase to draw a following noun.
For instance, in the Google Ngram results for "met at a hotel" versus "met in a hotel," in the first ten results for the 1987-1998 time period, "met in a hotel" was followed by a noun—suite, elevator, bar, room (three times), and restaurant—seven times. In contrast, "met at a hotel" for the 1938-1998 had only one following noun (suite) in the first ten results, although subsequent results offered such additions as garden brunch, swimming pool, and resort.
The phrases "stayed at a hotel" and "stayed in a hotel" were far less often followed by a noun in the Ngram results than "met at a hotel" and "met in a hotel" were—in fact, I didn't see any examples of a following noun involving "stayed at a hotel"—but "stayed in a hotel" did occasionally show up as part of "stayed in a hotel room." The Ngram Viewer couldn't find any examples of "met at a hotel room," "met at a hotel lobby" "met at a hotel bar," or "stayed at a hotel room." It found "in" versions of all of those phrases.
These results lead me to hypothesize that, overall and in everyday usage, the phrase "in a hotel" lends itself to further narrowing by a following noun (especially room) to a significantly greater extent than the phrase "at a hotel" does—and that this phenomenon muddies the waters when it comes to deciding which simple phrase ending in the noun hotel ("at a hotel" or "in a hotel") is more common.
Also of possible interest is the fact that, while Ngram found more matches for "stayed in a hotel" than for "stayed at a motel" and (by a very small margin) more matches for "met in a hotel" than for "met at a hotel," it found considerably more matches for "stopped at a hotel" than for "stopped in a hotel." This suggests that the preference for "at a hotel" or "in a hotel" depends to a significant extent on the preceding verb.