What is the closest alternative to "rubbish" in American English?
Solution 1:
Garbage is suitable, I think.
Solution 2:
First of all, the word rubbish is pretty well understood by American English speakers, and although it does have a British flavor it is used occasionally by Americans. So if you are worried that your use of rubbish will not be understood, that is less of a concern than with some other Britishisms.
Second, I’m not sure how rubbish is used as an adjective. All the uses I know of are nouns. Even in uses like “what rubbish quality” or “getting the occasional play on rubbish indie radio shows”, the use is as an attributive noun.
Finally, as others have noted garbage can be substituted for nearly any use rubbish, whether literal or figurative.
Solution 3:
The questioner should give an example of the kind of usage he/she is after. For example, if you want an equivalent exclamation for the British speaker's "Rubbish!" as an American I'd say "Bullshit!" if the situation is informal and "Nonsense!" if it's more formal, with lots of alternatives in between. But none of these would be parallel to the 'crappy' option that the questioner is intuiting.