We have extensive signed bike routes in Tucson, that include the shoulders of 4-6 lane roads down to residential neighborhoods.
I tend to avoid the main cross-town residential route as the pavement is really bad, and take my chances on a larger and busier street that has fairly wide bus/bike lane for about 5 miles. The city has nearly finished "The Loop"- a multi-use path that encircles Tucson, with an extension north along the Santa Cruz River. When I commute by bike to work once or twice a week, I now take the longer route (11 miles) that keeps me on the path for about 1/3 of the way rather than taking the 10 mile route with more traffic and potholes. I don't like to ride portions of "The Loop" on weekends when it is full of dogs, kids and inattentive walkers and runners. But for the most part, I just choose the routes that tend to have the combination of being direct and a wide or smooth bike lane, wheter it is a larger street or a neighborhood.
2016 Specialized Ruby Comp disc - Ruby Expert ti 155
2010 Surly Long Haul Trucker - Jett 143