Don't be fooled by Giovanni's mention of Nashville in line 9 (where the radio station was located). The library and Mrs. Long were located in Knoxville, Tennessee. We know this because Giovanni mentions Gay and Vine Streets, two main thoroughfares in Knoxville. Other things, like Giovanni's biography and the inclusion of the JFG coffee sign (4), help us to locate this place pretty precisely. (You can take a look at the actual library here.)
The time frame is a little harder to pin down, but is likely somewhere between 1952 and 1958, when Giovanni was around 8-14 years old. Knoxville was a desegregated city by then (one of the first in the South), but only newly so. Discrimination, as we see in the poem, lingered on. If she really was so very young, color us wickedly impressed with her choice of Leaves of Grass and the philosophical works of Alfred North Whitehead.