ABINIT can now be run, by anybody, on a virtual facility in the USA, called Nanohub

Nanohub is an NSF sponsored project to make HPC and educational resources available to the general public. After registering you can run a variety of ab initio and other softwares, directly on the cluster behind the web interface. There is also a lot of teaching material, tutorials and courses.

Execution times are fairly limited, but you will get direct access (e.g. along with a class of your students) to an efficient computational infrastructure, with a graphical tool to set up, run, and analyze ABINIT calculations. Cool!