Lorraine Hansberry's A Raisin in the Sun is set between 1939 and 1959. Hansberry does not pick a specific date for the play to suggest that the dilemmas that the Younger family face are ongoing plights for African American families during the time. The Youngers live in a small apartment in Chicago and strive to move to an all-white suburb, the only area in which they can afford to buy their own home.

The setting of the play is the Younger family apartment.  It's a very crowded place.  Walter Lee and Ruth have one bedroom, Beneatha and Mama have the other; Travis is relegated to sleeping on the couch in the living room.  They share a bathroom with other tenants in the building.  They have lived here a long time, but all have versions of a dream of moving to a bigger and more sun-filled place, especially Mama and Ruth in terms of the latter dream.  The play is set in Chicago, in the late 1950s.  

The family characters (referencing your second post) include:

Mama/Lena Younger - the matriarch of the family, is preparing to retire from domestic work on the strength of the insurance check of her late husband, Walter Senior.

Walter Lee Younger - her son, works as a chauffeur but wants to open a liquor store.

Ruth Younger - Walter's wife, works as a domestic, is pregnant (but this is not known at the beginning of the play).

Travis Younger - Walter and Ruth's son.

Beneatha Younger - Walter's sister, goes to college, wants to be a doctor.

Other characters include:

George Murchison - a college boy who is dating Beneatha, painted as an assimilationist.

Joseph Asagi - also a college boy who is dating Beneatha, from Africa, wakens Beneatha's interest in her heritage.

Mr. Linder - representative of the Clybourne Park neighborhood association.