General synonyms:
* Proverb
* Saying
* Expression
* Phrase
* Turn of phrase
* Collocation
More specific synonyms:
* Slang (for informal idioms)
* Cliché (for overused idioms)
* Aphorism (for short, witty idioms)
* Maxim (for wise idioms)
The best synonym depends on the specific context and meaning of the idiom you're trying to replace.