South Tel Aviv is in Tel Aviv.
When referring to "South" Tel Aviv, people commonly mean the part of Tel Aviv which is south to Yehuda Halevi and Harakevet streets - excluding Jaffa which is considered a separate part, although it is also "below" those streets. South Tel Aviv has been neglected for decades, rendering large parts of it an industrial urban wasteland. However, since the early 90s, and following a massive housing price increase in central Tel Aviv, an excelerated gentrification process has changed the face of many areas in south Tel Aviv - as many artists, students, and eventually middle-class (and in some cases upper-class) families moved in. Another factor greatly affecting South Tel Aviv's character is the influx of migrant workers from Africa, China and Southeast Asia, whose presence diversified the area significantly.
By Train - The "Haganah Train Station" serves Tel Aviv's southern neighborhoods.
By Bus - Any bus from within or without Tel Aviv that heads towards the Central Bus Station is sure to drop you smack in the middle of south Tel Aviv.
South Tel Aviv is not the quintessential tourist spot, but it is a fascinating urban landscape with notable nightlife interests and a chance to encounter Tel Aviv's bustling migrant community.
In the south of Tel Aviv the main place you'd like to go for drinking is Florentin neighborhood, especially around Vital and Florentin Streets. About 30 small places, mostly pubs, on area of only few hundreds meters.There are also few restaurants, great pizzerias and gelaterias. Everything is open almost till morning. The place is less known to tourists and has a "local" touch of small neighborhood with young population(therefore the prices are lower than in the center and beach area). It's not a sight-seing place so it's better not to go there during a day when it's quite boring and noisy. But it changes completely at night and then more than worthwhile a visit.