Sidewalks are for walking.
So take your bike for a walk.
In San Francisco, it's actually against the law to ride a bike on the sidewalk. However, there are some city streets with neither bike lanes nor sharrows where it's downright scary for a cyclist to ride alongside cars (I live at the corner of such a street).
Providing no bike lane on highly car-trafficked streets therefore gives the cyclist no options - one must stop, dismount and walk - defeating the very purpose of being on a bike!
In these situations, what's a city cyclist to do? Abide the law or defy it?