I am currently pursuing a juris doctorate at an American law school, with a concentration in international and comparative law. I would like to pursue a career in public international by working with an international organization or NGO in Europe. I am considering doing an LLM in International Law post-JD, but I am wondering if it's worth it or what would be the best route to navigating a career in international law with an American JD? All advice is welcome in this thread.

I’m not sure about job prospects, but there are a lot of variables here at play. Once you’ve got a US law license, you can take the QLTS in England or QLTT in Ireland, then you’ve got a law license (solicitor not barrister) in a European Union member state that has some reciprocal recognition in the rest of the EU. How the EU will treat English solicitors now that they’re getting an EU divorce is a mystery now, but bear with me. 
An LLM is a bit of a gamble no matter what, who knows what doors it opens up, but getting licensed in the U.K. or Ireland is a possibility with Your credentials if you just do the right exams to get the license. So practicing there is possible.