How do I make store searches work with WordPress?

It's very high-performance and comes with a map, but
https://superstorefinder.net/
is available.

https://superstorefinder.net/superstorefinderwp/addon/custommarker/info-window-icons/
I think I can do it to some extent if I can express the map in the worst minimum using these.

Just to advise, be careful when you are told that you want to create a site like 〇 の.
Whether it is a UI like 〇 の or a function like 〇 の, this area tends to be very ambiguous.
Also, even if the store function is called a store function, it is further divided into functions that search for stores and categorize stores.
Also, is it a function to search by zip code?Is it a free text search function?You will need to further refine your requirements.

Even if a customer tells us that they want to create a site like 〇 の, let's decide the requirements not like 要件 の, but like "store search function using zip code" or "CMS function that can be categorized and expressed by region.The stories around here are expressed in terms of "requirements definition" and "basic design" and are mentioned in various books and articles, so please refer to them.