I use Map My Ride Plus, which I got on sale for 99 cents. I was told it could suggest routes, but it seems to suggest workout routes rather than "Take this and that to get to Grocery Store X". Also, it takes some time to get started. I'd have my bike out, ready to ride, and be stuck waiting for the app to start up before I could hit the Start Workout button.
Still, it's a nice convenience to get some idea of what kind of workout I got from riding my bike (miles, calories burned, etc.). No idea how accurate it is. I heard about Strava too, but it apparently can't map your ride while you ride.