A map from the Billings Gazette shows the amount of bars per capita in every state and county. 

According to the breakdown:
In the state of Montana there is one bar for every 1,633 residents, thereby making it of the STATES WITH THE MOST BARS IN THE NATION. North Dakota holds the title for most per population density.
In the 2013 study Montana had a population of just under 1,000,000 people and 602 establishments.
New Hampshire and Georgia were two with the last amount of bars.
See the full map, along with drill-downs of each county here.