I have a MySQL database on Amazon RDS. When I created this database I unselected the "public access" option which can not be changed after creating the database. This means that my database instance can only be accessed from inside the VPC.
So now I would like to access the database in my local computer with setting the MySQL host with a EC2 VPS I have inside the network with access to the database. I want this server to act as my MySQL server so I can access it locally.
I just had to do this same thing. The process is to set up an SSH tunnel through the EC2 instance to the database. I wrote a post about the whole process that should be helpful