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!