In my experience there are people in many cities who are well positioned to help non-profits find Board members. For example, in Los Angeles that person is Carl Terzian. As part of his PR firm's services, he matches up firms and companies who want to find non-profits to support and non-profits that need board members. For example, for most business service firms, like law firms and accountants, being on a non-profit board is part of their marketing. So you might look for organizations who might have a tie-in to the purpose of your non-profit.
I agree that the selection is critical. The role of the Board (whether strategic, tactical, volunteer activism, fund-raising, etc.) needs to be made clear, and the personalities need to mesh. The Chair plays a critical role, because they can attract or repel good potential members. One way to do this is to be clear about the future of your organization, what does it plan to accomplish. Then you can ask what skill sets and resources you will need from Board members. For example, I am a change agent. I am attracted to non-profits that require an alteration in how they are operating. I stay around until the alteration is self-generating and no longer vulnerable, and then I move on because a different type of Board member is then needed and I am needed elsewhere.