Oooh, tougher than it seems at first glance. Let's see...assuming the river Shirebourne separates South from East Farthings on the more easterly section where the two farthings share a border...
1. Longbottom
Fellowship of the Ring, Prologue, 2 Concerning Pipe-weed, and The Two Towers, Book Three, The Road to Isengard (a rare text reference, as you noted, hope)
2. Pincup
Fellowship of the Ring, Prologue Map of A Part of the Shire
3. Sarn Ford (we really only know this as a river crossing...it might not be a town, but it's accorded the same prominence as Longbottom on the map)
Fellowship of the Ring, Prologue Map of A Part of the Shire
Several mentions of Hornblowers, and one also of the Sandyman family owning South Farthing land, but of these three, only Longbottom is mentioned as a place where people live.
I've not checked Lost or Unfinished Tales for any other hidden nuggets.