I simply plant the rest of the area in question, so that there is no question of having to mow anything at all. For a quiet, smooth area, that will be used as a passageway from one garden area to the next, I use a low ground cover like creeping thyme. This will stand moderate foot traffic, and the variety I favor, a lemon scented cultivar, releases a fresh, citrus-y aroma whan walked on. If I am dealing with a slope, I tend to plant daylilies, which are beautiful in their own right, have nice foliage and do a smashing job of holding the soil together. If I am dealing with what is simply a huge expanse of yawn-inducing green, I plant shrubs.
Shrubs come in an infinite variety of colors and textures.
Some flower, some provide winter color, and may provide berries that help the birds through the winter. And then I tuck flowers and groundcovers around those. Hellebores love light shade and pop into flower even before the daffodils have made an appearance. Long before the lawn turns from dead buff to green. So far I've managed to do away with about half an acres worth of grass this way, which leaves my husband time for more important things like building me a greenhouse.