Summarizing local alcohol regulations simply in one map is a real challenge, but this one on Wikipedia does a pretty good job. Exactly what the yellow shading means varies a lot by state, but it's a good place to start.
Dry county
A dry county is a county in the United States whose government forbids the sale of any kind of alcoholic beverages. Some prohibit off-premises sale, some prohibit on-premises sale, and some prohibit both. Dozens of dry counties exist across the United States, mostly in the South.
en.wikipedia.org