This map is poorly-done -- why use two colors to represent univariate data? (the yellower the state, the more restaurants per capita) -- but interesting nonetheless. The differences between states are all pretty minor -- DC has the most with 0.4 restaurants per 100 people, and Utah the least with 0.19 R/100. The DC estimate is probably skewed since the DC restaurants are serving proportionately more tourists. Montana, on the other hand, which has a very high number of restaurants per capita, I don't know how to explain.
Statemaster has the complete list. (Hat tip to the Door.)
