I have a back yard no shade and the grass is not in best shape!

How about creating a rock garden? You lay down all sorts of succulents there that don't require sun. It's low maintenance and really will look lovely.

Since the grass doesn't want to grow there...put in a beautiful raised rock garden by stacking slate rock or using stackable bricks sold at the Lawn & Garden stores. Plant the type of plants that seem to grow well in that location already; pick up the rocks that already exist [that you seem to stumble over] as you dig around & toss them into the 'bedded areas'...so you will have a real 'rock garden' & pick out a few longer rocks as display pieces or place statuary into the beds & surround them with rocks. After a year or so you will be surprised at what plants voluntarily grow there!

Get an unbrella or two so you can enjoy your yard and while taking breaks from daily chores or while building your rock garden.

We have the same problem....terrible soil and grass just won't grow. We have started building a variety of raised beds and bringing in fresh soil to fill them. Some of the beds have shrubs, some have flowers, some have vegetables, some have herbs, etc. You can choose whatever plans you enjoy and this will add curb appeal and freshness to your yard.