MHGS has an extensive collection of city directories for the Wichita and suburban parts of Sedgwick County.
In paper form, we have the Wichita directories from the 1800s through 2006, the Sedgwick County suburban directories from 1957 through 1995, telephone and criss-cross directories from the 1930s through the present day. You can find most of these in the library catalog: City Directories (Don’t be alarmed if the main page says “no items” — that just means that these items are not available for check out.)
We also have several digitized or transcribed directories: