In the previous post I showed that the difference between the summer solstice and the day when the latest sunset occurs varies by latitude, with a very small difference near the arctic circle and a very large one near the equator. Since a character in this XKCD comic states the difference is six days, we can narrow down the range of latitudes the character is talking about.
Here's a plot of the number of days between the summer solstice and the day of the latest sunset, by latitude:
A difference of six days falls here:
That covers latitudes 41.3°N to 45.3°N. In North America, that covers this area:
The characters in the comic are speaking English, and outside of North America this range of latitudes doesn't traverse any dominantly English-speaking countries, so it seems reasonable to assume the comic takes place somewhere in the above part of the United States or Canada.