The first thing you probably want to do is disable the default administrator user and create a new admin user. It's not uncommon to see failed SSH login attempts on Linux instances on EC2 and you'll likely see similar failures in your security event log if your security group is open to the world.
You probably want to restrict the security group allowing RDP access to specific IP blocks if you can't predict the specfic IP address you are connecting from.
Reviewing Amazon VPC or setting up your own VPN using an OpenVPN server are other options you might want to consider