Optimise a local landing page for a seed keyword, optimise GMB, build citations and perform a citation cleanup on any that are pre-existing. That usually does the trick. Consistency is key in terms of your NAP.
Analyse the SERPs for the ‘near me’ terms you want to target. Review and audit the page one listings to develop the keyword, content, on-page SEO and off-page SEO strategies to outrank them.
In most cases, about half of the results are going to be from niche authority websites (Yelp, Angieslist, HomeAdvisor, Avvo, RealSelf) as opposed to a single small business so if they’re trying to rank a specific businesses website for a near me search around a specific city (i.e. carpet cleaning company near me searched by someone in Forth Worth, Texas), you might be fighting against the “search intent” of that search query.
This happens a lot with “best” searches were Google doesn’t show a single entity, but a list of them since the searcher is still weighing their options at that point.