Graphhopper: An open source routing library and server using OpenStreetMap
github.com
github.com
I’m happily using https://www.magicearth.com which does offer both in a nice app, the map data is based on OpenStreetMap.
> Other map data will need a custom import procedure, see e.g. Ordnance Survey, Shapefile like ESRI or Navteq.
There is a project here for importing ESRI Shapefiles: