The second option can be hosted at ArcGIS Online without you doing anything (i.e. loading anything). It is a REST API. Yes, it is hidden in their stupid docs.
The third option is faster than anything else, but would require you to load planet-osm.
Ha, didn't know that. I'll look deeper into the docs then. Thanks!
What I meant is the ability to generate them via an API without having to handle any GIS / routing data yourself and this for any city.
Handling these kind of services takes a lot of time, especially if this is only a sub-part of a more generic product.
Thanks for the alternatives though