Is it correct to use "at" followed by a place name (city, town, village, etc.)? I've been seeing phrases like "a hotel at Las Vegas" or "she was living at London" quite a lot recently. Is this a difference between British and US English, perhaps?
The choice of in or at with a city depends on how speakers conceive that city in the context of the statement they are making.
If the city is conceived as a two-dimensional place in which to live and work, then in is the usual preposition. If, on the other hand, the city is conceived as a single point rather than as a place with dimensions, then at is the common choice.
This explains the difference between sentences such as:
I live in Frankfurt. / The plane stops at Frankfurt on the way to Seoul.
The meeting took place at Potsdam. / There was an explosion in Potsdam yesterday.
On this basis, the expressions a hotel at Las Vegas and she was living at London are the idiosyncratic choices of individual speakers. I am not aware of any significant patterns of difference between BE and AE speakers.
We use the word "At" for a stop on a journey: We stopped at a nice village. The train to Manchester stops at Birmingham.