With enough research as suggested above, you can usually pick a pretty good route thru a city. Some have bike trails that may help. Shown in green with Googles' cycling option. Many times it'll be through neighborhoods with stop signs if you are determined to avoid trafficed thoroughfares. You could also call a local bike shop or a Warmshower host for ideas for navigating a city.
I recently avoided a busy thoroughfare in Little Rock using Google street views. It was a through steet, but not nearly as busy as the alternative that had been suggested by a friend. The route I took was through a 'sketchy' neighborhood, his description. I reasoned it was
midday and the homeboys would still be in bed.