Thank you in advance for any replies, context, or ground truth provided.
Are you asking for a Point of Interest listing (i.e. an API to let you look up the nearest Target, Walmart, etc.?)? If so, https://developers.google.com/maps/documentation/places/web-... is one. There should be others.
Or are you asking for a way to render multiple locations of your OWN stores on a map and such? In that case, I don't think you need a whole SaaS, it's usually just a part of your frontend. e.g. for Wordpress there's a bunch of plugins (https://wordpress.com/plugins?s=store+locator), and similar exist for Shopify, Wix, etc. You can also build it yourself with Google Maps (https://developers.google.com/codelabs/maps-platform/google-...) or AWS (https://aws.amazon.com/blogs/mobile/build-a-serverless-store...) or Leaflet (https://leafletjs.com/examples/custom-icons/) or OpenLayers (https://openlayers.org/en/latest/examples/icon.html) or Mapbox (https://docs.mapbox.com/help/tutorials/building-a-store-loca...).
There are also commercial hosted offerings (just search for something like "embed store locator").
Is that kinda what you're looking for, or...?