Zoysia grass will not be a good choice for your climate. It is a warm season grass that will not green up until well after warm weather arrives and will turn brown with the first frosts of fall. You would be better off planting a cool-season turfgrass. And although you're technically in USDA Zone 5 or 6, you may want to choose plants hardy to Zones 3 or 4 simply because you have such a short growing season. Check out our plant encyclopedia at http://www.bhg.com/gardening/plant-dictionary/ to search for plants that fit your requirements.