There are many synonyms that can be used in place of the phrase "goes on town." Some examples include: heads into town, ventures downtown, goes downtown, visits the city, explores the city center, hits up the urban area, journeys to the metropolis, wanders through the downtown district, strolls around the city, meanders about the cityscape, or treks into the urban terrain. Each of these synonyms carries a slightly different connotation, so it's important to choose the one that best fits the intended meaning. Regardless of which synonym is used, all convey the idea of someone traveling to a central, urban area for social or commercial purposes.