Do Maps Rank on Their Own?

Here you are asking about ranking on Google. Doing your research ahead of time for the topic you are creating the map around will tell you exactly what Google is ranking for it. So always best to start by doing a search on Google for that topic (ie. Pet Stores in [city state]) and seeing what is ranking. You need to provide as much or more information than what you are finding with this search.

Typically, a simple map will likely not rank on it’s own. What is best is to embed the map(s) onto a page on a website. This allows you to add significantly more information so that you can keep your web page visitor engaged. This could include information that would be difficult to show on a map itself, links to other parts of your site, advertising, etc.

Ranking with maps is still going to require you to follow the SEO guidelines that Google provides in order to rank. But it will be much more likely to do so if attached to a website with current authority and for local businesses and address.