This tool can display on the OSM map as geo-markers:
Wikipedia articles which have coordinates for all language versions of Wikipedia
wikidata, wikipedia, and wikimedia tags from the OSM map database
Wikidata items which have coordinates
And now I added the possibility to display also the Wikimedia Commons categories which have got the geographical coordinates.
The tool is available via this link: http://ausleuchtung.ch/geo_wiki/
I created it for my personal needs, for my surveys, but, perhaps, it could be useful to others.
The tool is as simple as it could possibly be. Just click on the map and the geo-markers will appear on the map up to 10 km around the click.
In areas with many categories it makes sense to reduce the radius of the search, because the maximum number of displayed categories I limited to 100.
P.S. Only categories which are connected to a Wikidata item or Wikipedia article are displayed. I do not know how to display absolutely all categories with coordinates via MediaWiki API, or if it is possible at all. On the other hand, the categories which are not shown are usually the sub-categories of those main ones which are displayed.
But it is possible to add the tag wikimedia_commons=Category:* to an OSM object, and then it will be displayed via search in the OSM database (the 2nd option).