When I'm working with something that has that many straight lines, I like to add curves. Like concentric circles. I usually trace around a quarter for the first ring, then use my presser foot as a guide to quilt consecutive rings around the first one. Looks kinda like water drops on a pond. I like to do just one 'water drop' on small quilts, and up to 3 or so on larger ones. It can be a little bit awkward if the quilt is a large one though-turning it a lot.
Just quilting diagonal, sort of wavy lines from corner to corner (or edge to edge) looks nice too. You get a sort of curvy diamond look if you quilt both directions.