Proximity search software - Finding the nearest point

Hi, everyone,

For sales in my work, I am looking for a proximity search software with which I can add a radius to points on a map and find the next points I have set with one click on the map. You can think of it something like this map from OpenRouteService, where you can display the nearest vaccination center:

In my case, which software can you recommend to me, one who can create such maps and make them available to others?

Thanks in advance.

Best regards