"At the kiosk, you can buy beer at night."
Translation:Am Kiosk kann man nachts Bier kaufen.
Sounds fine to me.
Sometimes you can shift these prepositions around a bit; generally it tends to work like this:
When you buy something "at a tradesperson's", you need to use "beim Bäcker / Metzger / Klempner / Friseur" ("at the baker's / butcher's / plumber's / hairdresser's").
When you buy it "at a business", it's "in der Bäckerei / der Metzgerei" ("at the bakery / butcher's shop"), "im Kaufhaus / Bauernladen" ("at the department store / farmers' shop [a place that sells products of local farmers]".
Then there's "am Kiosk" and "an der Tankstelle" ("at the gas station"); to me it feels like these refer to the location/building itself.
When you buy it at an "event", it's "auf dem Markt / der Messe / der Kirchweih" (at the market / trade fair / country fair).
Further to my comment of about four minutes ago, I gave up on giving an answer in German and entered one in English. The English answer was rejected too. The program did not like my syntax and rejected my answer. (I am a native speaker of English and hold, among others, a degree in English from an English university.) This is just frustrating and really rather pointless.