A straight-line option other than SID is to stitch down the middle of each log (less stitching per log and fewer seam allowances to deal with). Another straight-line option is to do something like a Greek key design where you start in the middle and then spiral out.
Geometric designs such as log cabin often benefit from circular type quilting. An old-fashioned option is the Baptist Fan option. I love that one in old quilts; however, it does mean crossing a lot of seam allowances.
Nowadays many people put feather designs in the light areas. I like that too.
Try Googling "log cabin quilt" and then click on "images" to see how some of the different options look.