The roots of Black Walnut (Juglans nigra L.) and Butternut (Juglans cinerea L.) produce a substance known as juglone (5-hydroxy-alphanapthaquinone). Persian (English or Carpathian) walnut trees are sometimes grafted onto black walnut rootstocks. Many plants such as tomato, potato, blackberry, blueberry, azalea, mountain laurel, rhododendron, red pine and apple may be injured or killed within one to two months of growth within the root zone of these trees. The toxic zone from a mature tree occurs on average in a 50 to 60 foot radius from the trunk, but can be up to 80 feet. The area affected extends outward each year as a tree enlarges. Young trees two to eight feet high can have a root diameter twice the height of the top of the tree, with susceptible plants dead within the root zone and dying at the margins. The juglone toxin occurs in the leaves, bark and wood of walnut, but these contain lower concentrations than in the roots. Juglone is poorly soluble in water and does not move very far in the soil. [From Ohio State University Extension Fact Sheet HYG-1148-93 by Richard C. Funt and Jane Martin] The Ohio State University Extension and the American Horticultural Society have reported that R. nudiflorum, Pinxterbloom Azalea, and Exbury Azaleas Gibraltar and Balzac will grow near Black Walnut and Butternut trees. They also list many other plants that will grow in the root zone of these trees. If you look at the chart, blueberry (Vaccinium) is not on this list. So if you have black walnuts, then don't use the soil around blueberries. Here is a link that might be useful: Plants compatible with black walnut.

To totalchaos: Thanks for the tip. I must admit, I never would have thought of that. But it sounds promising. I especially like the point that they're drought tolerant.

Not sure about dog proof, but here's some things that are suppose to grow under and around black walnut. astilbe, bee balm, begonia, bellflower, bergamot, bloodroot, Kentucky bluegrass, spanish bluebell, virginia bluebell, bugleweed, some chrysanthemum, coral bells, cranesbill, crocus, shasta daisy, daylily, dutchman's breeches, ferns, wild ginger, glory-of-the-snow, grape-hyacinth, herb robert, hollyhock, hosta, hyacinth, siberiean iris, jack-in-the-pulpit, jacob's ladder, jerusalem artichoke, lamb's ear, leopard's bane, lungwort, mayapple, merrybells, morning glory, narcissus (some) pansy, peony (some), phlox, polyanthus primrose, snowdrop, solomon's seal, spiderwort, spring beauty, siberian squill, stonecrop, sundrop, sweet cicely, sweet woodruff, trillium, tulip, violet, virginia waterleaf, winter aconite, zinnia.

http://www.ext.vt.edu/departments/envirohort/factsheets2/tree/dec94pr1.html The Virginia Coop. Ext. Serv. used to have a publication titled "What grows under black walnuts?" cited above. Unfortunately, the link no longer works. Try to contact them directly or use the Wayback Machine.