I use the bike route given by Google Maps as a starting point. Then I get into Street View so I can really see where I'll be riding. Is there a bike lane? How wide is the shoulder? What's the condition of the road? I like riding on roads with bike lanes or wide shoulders (where I don't care if cars are flying by me), if possible. Some of the popular routes in my area are on roads with tiny to no shoulders and 55mph speed limits. Sorry, not interested. I have yet to find any mapping site/app that finds a route that I am always happy with. They all need tweaking. I just find that Google Maps gives a good starting point and has the tools to let me come up with a route that I'm happy with.
Cycle apps using OpenStreetMap will try to find the safest routes. If using Citymapper you can explicitly choose between faster or safer (slower) routes. OSMAnd let's you choose particular types of lane.
