We have been Finally Successful in Installing Web App Builder Developer Edition on our City Computers.
We followed the instructions on the Web App Builder for Developers Website. But we kept getting the E connection refused error.
Found this article in the ESRI help 43741 - Set a proxy in the Web AppBuilder (Developer Edition)
But to make it easier for non programming folks just change this line
START "Web AppBuilder for ArcGIS" /B %nodeFile% %serverjsFile% -proxy="PROXYNAME:PORTNUM"