Near-me results are generally driven by the searcher's current or inferred location plus relevance and prominence. A business does not need to repeat 'near me' throughout its website to qualify.
What this means in practice
Treat this as one part of a broader search-visibility system. The best next step is to verify the current site and profile data, compare it with the actual search intent, and make changes that improve clarity for customers as well as search and AI systems.
Allen Ink generally prioritizes fixes that affect the largest number of pages or customer touchpoints first, then builds supporting content, local authority, reviews, and measurement around those foundations.