I want to go for a short cycle tour but I want to avoid main roads. Is there an app for that?
For UK based routes (this is where I think you are, judging by your profile) you can use CycleStreets. It’s also available as an app on most phone platforms (Apple, Android, Windows Phone). Input your start and end points then when you get a route select the "Quietest Route" tab. That should give you either cycle paths or quieter roads.
I've always quite liked http://cycle.travel - UK oriented but the map interface is OpenStreetMap based so can handle overseas as well. Website not an app, but may still be useful.
It defaults to low-traffic-roads (calculated from known traffic data, not simply road classification) and includes a very useful height mapper display, so you can tweak a proposed route to avoid steep hills.
It also offers randomly generated "short tours" - given a defined start point and distance, it will try to come up with possible cycle routes in the local area. For example, "twenty miles round trip to something near Cambridge", or "a hotel fifty miles from Leeds with a route there and back". Quite a clever idea, IMO, though I've not tested any of them out...
I use Strava for ride route mapping, and it works okay. Some local knowledge helps avoid possible pitfalls.
It doesn't specifically avoid main roads, but the "use popularity" switch will favour roads where cyclists go. You can also "minimise elevation" if you would rather go around than over something.
Example - here's our planned lunchtime route at work tomorrow. https://www.strava.com/routes/4970649
Google Maps has that capability. It is probably not the greatest in the world, but free, and many people have it anyway.
After you have chosen you target and directions as usual, you can switch to different locomotion modes; car is on the very left (and the default), but there is also public transportation, pedestrian, bicycle, and plane.
in addition you should probably choose the option 'avoid main roads'
My experience is that it is pretty good (good enough for me, I use it)
TomTom (App, Hardware Devices) have the capability to choose "winding road". This is mostly aimed ad motorcyclists, avoids busy roads and tries to choose "interesting" roads instead. I would assume that these routes are also better suited than normal car navigation.
Also choosing "shortest route" on navigation systems gets one usually away from big roads.It also seems to be a pretty reliable way to meet mapping errors ... which shouldn't be a problem on a bike most of the time.
Specific "cycling modes" so far semm only work in well mapped urban areas of the western world.