Well, if you do not know where she got married, then I suggest you file a Motion to Vacate the Alimony and use the fact that she is "Cohabiting" with this person for however many years which changes the circumstances.
Once you have something pending in court, you can file Discovery to have her present the documents such as her income tax forms, That will show she has filed Married - and then you can request the marriage cert, etc
But you need to have a pending matter in the courts to get that information. There is no way to just find it out, unless you hire a private investigator who can maybe get the information for you
Your other option is to stop the alimony - let her file a Contempt Motion and that will be when she hangs herself
Of course, if you just stop then your recourse for reimbursement back to the date of the marriage is limited. So the best thing, I suggest is to file the Motion to Vacate.
If you need more clarification, please let me know by posting the question here. Please do not rate me until you are completely satisfied.