The trick to getting a fight isn't necessarily undermining the US Navy - you only need to make the other guy think that he can beat the Americans. To some extent, this is what happened in the Falklands: once Britain mobilised, the Argentinians were reduced to waiting for defeat or a miracle, but they didn't think the British would fight.
Find some tertiary theatre where the local power thinks that the Americans don't care enough about the matter at stake to send in an overwhelming force, and you've got a fight.
With that in mind, the obvious flashpoints won't do. You need the equivalent of the Falklands: something inconsequential somewhere nobody has ever heard of, much less has strong opinions about. And, given American views on the freedom of the seas, there are very few such places and fewer still have a fully-complemented harbour launch in their navy.
Best bet might be some tin-pot little African country (TPLAC) getting in a tizz over territorial waters - something like the US recognising a 3-mile limit whilst the TPLAC claims 12 miles - and arresting a US-flagged ship. During the inevitable freedom of navigation exercise, the TPLAC gunboat's captain decides that discretion isn't the better part of valour and opens fire on the US surface ship sent to remind them who's boss.
Which it does, with extreme predjudice.