There are a plethora of synonyms for the phrase "going to town." Some of these include "heading into the city," "going for a stroll," "taking a trip," or "embarking on a journey." Additionally, one could use "venturing out," "commencing an excursion," "exploring the town," or "going on an adventure." The phrase is often used colloquially to describe someone who is taking a task or project very seriously, so other alternatives could include "getting down to business," "tackling the job," or "working diligently." Whatever phrase you choose, make sure it conveys the intended action or purpose of the activity you're describing.