Two species are native to the Eastern USA. One species from eastern North America, Eriogonum alleni, is found in the very sunny and dry Shale Barrens Habitat in the Appalachian Mountains of Virginia and West Virginia. The other species is E. longifolium is from Rocky or sandy glades from southern Missouri and Kansas South to Texas.
Both are probably a little large for the average rock garden.
I hope to get to some shale barrens, here in Pa or further south sometime and get some pictures.