This translation doesn't seem as natural as "Where did you go day before yesterday?" Maybe not all English speaking countries speak the same way :)
How about "two days ago"? For me it sounds more natural than "the day before yesterday"
Their translation sounds the most natural to me out of anything else posted in the comments so far. - a Californian i.e. "The day..." sounds better than "on the day..." or just "day..."
Obviously ereyesterday should be accepted in case anyone over 100 years old is using the app.
"The other day" is too broad; it could refer to a day last week, last month, or even just yesterday. "The day before yesterday" is a single, specific day.