When one speaks about the setting, one must address both place and time.
The setting of place is most definitely the country of Nigeria on the continent of Africa. The reader can get even more specific in that the relationship between Nene and Nnaemeka takes place in the city of Lagos in a room at 16 Kasanga Street. When Nnaemeka goes to visit his father, the setting changes to an Ibo village in rural Nigeria.
In regards to setting of time in "Marriage is a Private Affair," we can assume it is a "fairly modern" setting; however, we are not told a specific time period. There is a city involved and a specific street, but there are also rural villages. Because there is letter-writing involved, it can be assumed that the story takes place before email was prevalent. Also considering that Chinua Achebe wrote the story in the 1950s, the reader can then infer that the time period is most likely the mid twentieth century. In regards to the interval of time, the story takes place over approximately eight years and involves the interval between Nnaemeka falling in love with Nene to Nnaemeka having two young sons who request an audience with their grandfather.