From the USDA Economic Research Service:
Food Access Research Atlas (link) presents a spatial overview of food access indicators for low-income and other census tracts using different measures of supermarket accessibility; Provides food access data for populations within census tracts; and offers census-tract-level data on food access that can be downloaded for community planning or research purposes.
State Facts Sheets (link) provide information on population, income, poverty, food security, education, employment/unemployment, farm characteristics, farm financial indicators, top commodities, and agricultural exports. Links to available county-level data are included.