First of all...
I think「来日する」means to be in a foreign location and return to Japan.
No, you're thinking the other way around. 来日 is "(for a non-Japanese person/group) to come to Japan". Only non-Japanese person/group (e.g., The Beatles) can do 来日. Returning to one's home country is 帰国する.
Likewise, 来米 means "(for non-American person/group) to come to USA", but Japanese people living in Japan do not ever need this verb for the obvious reason. But Japanese speakers living in the USA may use 来米 referring to someone coming to the USA.
You cannot combine arbitrary kanji to form a word, but 来-/訪-/在- and so on are exceptional. Basically you can pick an arbitrary one-kanji country name or prefecture name, and make a compound that means "to come to Brazil", "to visit France", "to stay in Korea", "to come to Hokkaido" and so on. Wikipedia has a list of similar verbs: 二字熟語による往来表現の一覧
However, most of them are rare, and used in stiff written Japanese. Only a few words are safe in conversations. I personally think 来米 would be safely understood in conversations if there is enough context (for example when the speaker is a Japanese businessperson living in the USA and is inviting his Japanese boss living in Japan). But when in doubt, it's always safe to avoid it.
See: Are there more terms similar to 上京 or 来阪 for going to Japanese cities?