This is a horticulture topic with little conclusive evidence either way regarding the real-world risk of juglone to plant health (compared to lab experiments). Juglone concentrations in soil will be highest below the drip line of walnut trees with lower levels some feet beyond the dripline.

You can learn more about one main counter-argument to juglone toxicity in this linked Washington State University publication. Juglone-resistant plant lists may differ somewhat or be incomplete for this reason -- observed vulnerabilities may not be consistent because of interference from soil microbes, underlying plant health prior to exposure, and other environmental conditions. The following web pages list plants and their relative tolerance to juglone (based on observations) :

Landscaping...Around Walnuts -- Penn State
Black Walnut Toxicity -- Wisconsin Extension
...Black Walnut Trees -- Cornell blog
Black Walnut Toxicity- Morton Arboretum Tomato is thought to be very sensitive to juglone- causes wilting and stunting. You could plant a few "sentinel" tomato plants in the area and observe their growth. No symptoms would indicate that juglone is not going to be an issue for you.

If you can't find your specific plants listed in the above information and are still searching for answers, please feel free to reach back out to us. 

Emily