This lovely short story takes place in the apartment of the two main characters, Della and Jim. Their apartment is small, with only two windows and the looking glass (mirror) mentioned. The narrator actually states, "Furnished rooms at a cost of $8 a week. There is little more to say about it." Other than that, the only other detail we get about the apartment is that even their mailbox is very small.
Really, the physical setting is not that important. What's more important about the setting is the time, which is Christmas Eve. This is necessary because it shows us the desperation that these two have when it comes to buying a gift for one another - they've saved until, literally, the last minute. Now's the time to buy the gift, and they're each still short. This is why Della sells her beautiful hair and Jim sells his precious watch.