I ride on residential neighborhood streets and dirt/gravel trails as much as possible. I know all the streets and trails around where I live and work and seldom have to resort to riding on high-speed boulevards with multiple lanes of cars going 45 mph or more. I cut through parking lots too, but they're not the really busy ones such as where grocery stores and gas stations are.
One I regularly ride through has a department store, a bank, and doctor's offices that aren't open yet when I ride through in the mornings, and another has a movie theatre and restaurants that aren't open for breakfast, so it's deserted too, except for some prep cooks' cars parked at the restaurants when I pass by.
My favorite is a shopping center that I ride around the back of, where trucks unload, but there is lots of room for me to stay far away from them. The best part about this one is the tall wooden privacy fence that separates the parking lot from the houses has a sidewalk and an opening for pedestrians, cyclists, parents pushing strollers, etc. I go very slowly here so I don't bowl over granny walking her teacup poodles on twenty-foot leashes or anyone else, and fortunately I rarely see anyone around there. That shortcut is my favorite, and I was really pleased when I detoured off my usual route and discovered it one afternoon. It saves me a lot of time, compared to riding around the whole block in traffic to get to the same place.