Precise location tag

If I have the precise location data of, say, the entrance to a restaurant or something, for a building which was previously put in with a loose approximation of the location, is there a way to change the geographical marker of this particular amenity? As in, can I enter the precise coordinates somewhere?

Not directly afaik, but you can save these coordinates as markers in a GPX file and open it in JOSM. These markers will then become visible in JOSM and then you can put a node on that position.

Right, so I’d place a new one and remove the previous entry.

You could do, or just move the existing one over your waypoint marker. If it’s a node just click and drag.

If you are using josm you can just open the .osm file in an text editor and search for the amenity and the replace the coordinates.

Thank you for your tips!