For a free webmap creator i would strongly advise you to try UMAP.
It's free, based on open streetmap data, and really easy to learn. I personnally use it at work with peoples who need to digitize spatial data but have no technical skills.
http://umap.openstreetmap.fr/en/
If you have lots of markers to depict, umap has a cluster function that is pretty usefull when you have to show lots of points.