Connect to SQL Server 2012 running on Azure VM via local SSMS 2012

You don't want to connect to Windows Azure SQL Database by using an IP address, you will want to use the logical servername you are assigned (something like fooxxxbar.database.windows.net).

Also, WASD only uses port 1433, you can't configure that (not today, anyway).

The firewall rules for WASD are for the client connections. When you first create your SQL database you will be prompted to create firewall rules and your current IP address will be listed as an example of an IP to allow.

HTH

I saw an item on Pinal Dave's blog recently that may answer your question. He suggests adding the line 127.0.0.1 localhost to your hosts file

The full article can be found here

I do note, however, the situation he refers to is a machine that is not part of a domain - if your machine is, then this may not solve it