I am trying to start a new SharePoint 2013 empty project in Visual Studio 2012. When I validate the URL to connect to the server, I get a connection error (see attached) . I am a Farm Administrator, and Site Collection Administator, but still can't connect and need to develop some apps.
If you are developing SharePoint Provider-Hosted Apps, then you don't want to do a SP2013 empty project. That is designed for a server-side WSP solution, which requires you to run Visual Studio on the SharePoint Server itself - so, to create an empty 2013 project you'll need to be on the WFE box.
Do you get the same error if you try to create an "App for SharePoint"?
Added I.P. Address and localhost to the hosts file. Also added to the DBObjects Owner groups in SQL Server.