Running Node or Python app from a Linux Azure VM

I can't seem to figure this out. I created a new Ubuntu VM on Azure and I can SSH into it. I installed Node (which I've done many times) and I tried to run the test app from nodejs.org:

var http = require('http');
http.createServer(function (req, res) {
  res.writeHead(200, {'Content-Type': 'text/plain'});
  res.end('Hello World\n');
}).listen(1337, '127.0.0.1');
console.log('Server running at http://127.0.0.1:1337/');

However, when I go to the IP (which is the same one I SSHed into the box from) + :1337 it just never loads. I tried :80 too, but still no luck. I also tried running python -m SimpleHTTPServer on :8000 and I still can't view the site. I must be missing something.

Just so you know, I'm just trying to setup a simple dev box with a bunch of projects on it. I want to be able to work on my projects anywhere. Some are 100% front-end JS projects so SimpleHTTPServer would be fine. Some are Node projects too. In either case, I just want to be able to hit some port and see what I'm working on.

Oh also I opened up the Azure firewall to the VM, redirecting traffic from port 80 to port 1337 (https://www.evernote.com/shard/s5/sh/3aef8e76-04f6-48cb-84f9-32462bc425a7/f0cd749773a9d09cee66d00fe3e707c0)