I must say that one of the interesting things about learning another language is that it forces you to re-examine your own. It's been a half century since I've had a grammar course and I wasn't all that interested in it then-so this one threw me for a loop. For those who are interested in this "adverb of direction" here's a link-http://www.englishcurrent.com/grammar/go-home-adverb-no-preposition/.
Homely is proper English. It is true that it isn't used in ordinary conversation a lot.
In North America, it is used to describe a woman who is unattractive in appearance but not really unpleasantly so. In Britain, it is used to describe a structure that looks or feels like a real home.
It is a good idea to check out a word in a dictionary before posting that it doesn't exist.