When riding a bike on a street that does not have a designated bike lane, is there a location of the street where the bicyclist is required to operate the bike?

Yes. Vehicle and Traffic Law Section 1234, provides that a bicyclist must operate the bike in a usable bike lane or if such a lane is not provided, “near the right-hand curb or edge of the roadway or upon a usable right-hand shoulder in such manner as to prevent undue interference with the flow of traffic except when preparing for a left turn or when reasonable necessary to avoid conditions that would make it unsafe to continue along the right-hand curb or edge.” It is important to note that in the City of New York, N.Y.C. Traffic Rules and Regulations provide that when there is no bike lane provided and the street is a one way thoroughfare, bicyclists may use either side of a street ride, provided the street is 40-feet wide or more.