My favourite of the ones I’ve used thus far, is Nils Sjöstrands Ny latinsk grammatik. It is print on demand, I am afraid, but from what I understand, they run new prints pretty quickly. It makes several inferences to the Scandinavian languages, as well as German, making it a very good tool.
The word "domus" means a "house". I think "domi" is both the locative case and the genitive case singular, so as well as "at the/a house"/"at home" it also means "of the/a house".
(I hadn't heard of the locative case until I came on this course. The locative for names such as Rome's - names that are declined like common nouns in the singular- seems to be the same as the genitive singular. Please somebody tell me if I'm wrong.)
There's an interesting discussion on the StackExchange website about how to distinguish "house" from "home" in Latin. The word "lar" was suggested in place of "domus" for one's "home". "Lares" were the household gods.
The fact that there's a special form for "at home" (with the locative case being used instead of a preposition and some other case) seems to suggest "domi" was how Romans said "at home", though.