In my experience any time a merchant tells me they don't take Amex, they actually do take Amex but the owner / manager doesn't like paying the higher merchant fees so refuses it since most people carry an alternative payment card. I generally insist, and actually if any merchant /does/ accept Amex and claims they don't, it's a violation of their merchant agreement and you can report them for this.

With the exception of international travel, while I'm in the US I generally /only/ carry my Amex, because it's as good as cash for any of the businesses I'd generally want to frequent anyhow.