We already have all the data we need to identify the parent state of each airport. The dt dataset includes the geo-coordinates of the locations, and we managed to render the states as polygons with the map function. Actually, this latter function can return the underlying dataset without rendering a plot:

> str(map_data <- map('state', plot = FALSE, fill = TRUE))
List of 4
 $ x    : num [1:15599] -87.5 -87.5 -87.5 -87.5 -87.6 ...
 $ y    : num [1:15599] 30.4 30.4 30.4 30.3 30.3 ...
 $ range: num [1:4] -124.7 -67 25.1 49.4
 $ names: chr [1:63] "alabama" "arizona" "arkansas" "california" ...
 - attr(*, "class")= chr "map"

So we have around 16,000 points describing the boundaries of the US states, but this map data is more detailed than we actually need (see for example the name of the polygons starting with Washington):

> grep('^washington', map_data$names, value = TRUE)
[1] "washington:san juan island" "washington:lopez island"
[3] "washington...