You can install a desktop environment on your droplet though there is not one installed on any of our images by default. This script can either be added to the user-data box on the droplet create page or can be run on your droplet once it is created. The script will install x2go, a remote desktop server along with the XFCE desktop environment on your droplet. While this script is targeted at Ubuntu 14.04 I just ran a test on a fresh Ubuntu 16.04 droplet and the script works as expected.

Once you've run that script on your droplet, download and install the x2go client for your operating system. You should be able to connect by default with the root user. If you received your root password via email you will need to log in once via ssh to set a new password before you'll be able to connect with x2go.