Experts and BHG readers answer.
You've got several options for your bare spot. First, if you remove the larger rocks and amend the clay soil with lots of loose, crumbly compost, you can grow just about anything you want in the spot. You could even just cover it with turf to blend with the rest of your yard. Another option is to create a sort of false rock garden. Most rock garden plants require well-drained soil, and your clay might hold too much moisture for them. But you could make the large rocks a feature and add plants like soapwort (Saponaria officinalis) and Sedum. If you're looking for shrubs that'll tolerate your rocky clay soil, consider spirea (Spiraea), mock orange (Philadelphus), or even a colorful but prickly barberry (Berberis). Magnolias, both tree and shrub forms, will also tolerate heavy clay soils.