GraphHopper? Not sure what it uses, I have no GSF enabled and it works.
I only have a problem with the location but I need to experiment more.
And yes, OpenStreetMap in a browser works nice too.
You can set how you would like to travel (car, foot, others) and even via anothe rplace if you would like.
GraphHopper can do this too.
On OpenStreetMap you can chose 5 or 6 different servies to calculate your route.