I have used this cheap, effective way of going short distances and ones that you do not have to worry about where you come out, with the long distances.
Affix a 1 inch PVC pipe to the end of a water hose and sharpen the end to a point. Dig a hole on both sides of the concrete walk way so that you can aim your borrer horizontally.
Turn on the ater and start pushing gently. the point of the PVC and the water pressure will errode out a cavern to the other side. Then insert your wire either in the cavern or in the pvc pipe and then carefully compact the cavern area with tightly packed sand to give the support back to the sidewalk.