I have a local REST API though I'm only really dealing with POST's.
mysite/api/ -> http://remoteSite.com/api/
so when my front end hits my endpoint with params the server would then post those to the remote server (3rd party API) and return the results to the original POST.
I've tried looking at Koa, Express, Axios, Bluebird but I can't seem to find a reasonable way to do it or a decent search term to find examples.
You are looking for a proxy.
If you have to use NodeJS, you could for example look into the node-http-proxy library:
var http = require('http'),
httpProxy = require('http-proxy');
//
// Create your proxy server and set the target in the options.
//
httpProxy.createProxyServer({target:'http://localhost:9000'}).listen(8000);
//
// Create your target server
//
http.createServer(function (req, res) {
res.writeHead(200, { 'Content-Type': 'text/plain' });
res.write('request successfully proxied!' + '\n' + JSON.stringify(req.headers, true, 2));
res.end();
}).listen(9000);
Here, localhost port 8000 acts as a proxy for localhost port 9000. You want to set this up to point to a remote server instead.
You could also look into the Apache web server or Nginx for alternative ways to set up a proxy, potentially with less effort and more stability.