To level up a town, you have to do Sidequest missions (a teal blue sword or book icon) that are on or around the Town icon. Once you do two or three of them, this initial level up achievement will unlock. Please note that more Town Sidequests will unlock as you progress through the Libra of Souls story missions.
Refrain from doing any Sidequest that says Bounty for Scoundels or In Search of Strength as these are optional and unrelated the Towns.