Why do you want to do such thing you may ask? Because I need to be able to make thousands of queries per day and I can imagine you guys won’t be happy if I directly hit your servers every time.
Now, I know how to download the data, how to import it in a database and how to make an API, but I have no idea how to render a map or draw items on it.
Basically I want to run my own geolocalization service without being tied to a monthly fee, if that’s possible.
For raster tiles (what the standard OSM layer uses) you may find switch2osm.org a good place to start. Or if you’re interested in exploring vector tiles see OpenMapTiles, Planetiler, or Tilemaker
Running a tileserver covering the whole world is generally quite resource intensive, but the costs can be kept down if only need a small area or don’t need frequent updates.