The kanji 郷 is not the only one with the kun-yomi of sato. Halpern says that with the same kun-yomi, 里 means “village.” Meanwhile, with the on-yomi of RI, 里 means either “countryside, country” or “village.” (As RI, this character once represented the Japanese version of a mile, as well.)
If this kanji looks incredibly familiar, but you don’t know why, it’s less likely that you’ve seen it as its own kanji and more likely that you’ve spotted it as a component in 理, which shows up in 料理 (ryōri: cuisine, cuisine + to manage). Or … maybe you remember it from my discussion of the Great Wall and the movie Riding Alone for Thousands of Miles.
The two sato kanji team up in the following word:
郷里 (kyōri: birthplace, hometown) hometown + countryside
Too bad this is an on-on combination. I would have loved a yomi of satozato! As the breakdown shows, Halpern differentiates the meanings of the characters in this compound, but sometimes I feel like such hair-splitting doesn’t mean much.