It's the white house with red trim, 1749 S Street. Hughes, his mother, and his step-brother rented two upstairs rooms there beginning around January 1925. He lived here when he worked for Carter G. Woodson, and it's where he was living when he revised The Weary Blues for publication at Carl Van Vechten's urging.
It's a pretty unassuming house, but I'm sure it's no "shabby apartment," as Arnold Rampersad calls it in The Life of Langston Hughes (vol. 1). A dozen years ago, that area was still full of affordable apartments and group houses populated by students; now three-story houses just across the street often list for a million plus change.
Hughes didn't live here long, and he didn't care much for DC, what with the allure of New York City and the ingrained segregation in the nation's capital, but he's an integral part of that network of African American intellectuals and artists who either lived in or passed through the District in the early to mid twentieth century.