I took a trip to Europe a few summers ago and wanted routes to run in each of the town/cities I visited.
I used Google maps to find the location of where I was staying, then to explore the area looking for likely looking roads. Since I was running, not cycling, I looked for things like parks and sidewalks instead of lightly trafficked roads and bike lanes, but the same theory applies.
Once I found a route that was the approximate distance I was looking for, I went into street view to ensure that the neighborhoods I was planning on visiting at least looked decent (there are a lot of places in the US where you can tell just by looking that it's probably not safe for a stranger in running/cycling attire to be passing through early in the morning).
I then printed out a map of the planned run. When the day of the run came, I did my best to commit the route to memory and off I went. I did get a bit off my track in Segovia, Spain, but managed to make it back "home" just fine. All my other routes I managed to run according to plan.
If you're simply exploring around the area you live, just get on the bike and explore! You should know your area well enough that even if you take a wrong turn somewhere you should be able to work your way back to a main road that you recognize in only a few minutes.
Take some sort of GPS tracking device with you - I've used Strava on my phone once or twice to find my way back, even when I was running near my office, missed a turn on a new route and ended up somewhat misplaced. The funny thing is, that ended up being a much better route than what I'd originally planned.