It's exact. Could we say that on Duo? But it's also referenced as a broth*l (lupanar) on wikipedia fr (the word caupona is not present in the eng version), and the article says it involved same gender, and on the eng. page there are very interesting swearing words in Latin, as graffiti. I won't teach them here, because I'm too respectful of neutral learning material for kids without any sexuality-related stuff, but you can see yourself if you are intested. Lupanar of Pompei on Wikip.
Cauponae as "strange" boarding-houses" confirmed.
Another possible translation is "cabaret", I reported it.
Of course, your translation should be accepted. I can only speculate that they want to hear "to me" because they're using the dative mihi here, not the accus. me .
But that's not a good reason. In my opinion, we can translate mihi as either "me" or "to me," depending (of course) on the demands of the English verbs used.
Thus, "Puella mihi appropinquat" could be translated either "The girl approaches me" or "The girl comes near to me." What's important is that the Latin demands a dative case with certain verbs (but it seems needlessly pedantic to require "to me" in the English translation).
I still feel like, "Another correct solution," is the real correct answer
I believe the "Another correct solution" is usually Duo's default answer for the exercise. In my opinion (and many other people's opinions), this is not always the best translation; it seems to be whatever the particular contributor who wrote the exercise decided sounded good, or sounded like a good grammar lesson.
There are multiple correct and perfectly good answers for most exercises, so read Duo's suggestion as exactly as it says it is: another correct solution, and not necessarily a better one. Sometimes Duo's default answers are a little odd, so your answer may even be better than Duo's suggestion. If Duo marks you right, you're right.
I wish they'd indicate whether they want "I like x," or "x is pleasing to me."
When there are multiple correct answers, Duo's suggested answer for a particular exercise is usually pretty unpredictable, since both answers are perfectly fine. There's no way to know which answer is Duo's default, so just understand that both answers are correct.
For this particular phrase, I would personally recommend always translating "mihi placet" as "I like," since that generally sounds better in English. It won't always be Duo's top choice, but it will still be right.
Notice that both the noun in the nominative case, the subject (caupōnae) and the verb (placent) are plural: -ae is the nominative plural ending (for 1st decl nouns), and -nt is the 3rd person plural "they" verb ending.
So, you have to say something like "The INNS in the city PLEASE me."