I need to renew my US passport as quickly as possible outside the US,?
Check the local US embassys website, download the documents you need and check the hours that their passport desk is open, fill out the documents and have whatever form of payment they accept, then go to the embassy at the correct time and get a new passport. I had to do a couple of things with my passport when I lived in London and it was quicker and easier to get it done at the US Embassy there than when I was back in the US.