As an electrical engineering graduate, what can I teach myself in my spare time that is typically not offered in the electrical engineering curriculum that will benefit me in the future?

I think is depoend in which area you want to improve. For example in case you work with power generation, then reading a manual for gas turbine and generators will benfite you a lot. As Iqbal said standard is essential part In case you want more academic courses, I advice you to check edx website and coursera

My friend, the best you can do in your spare time is study all related standards like IEEE, NETA, NEC , VDE or any other standards which apply to your specialty. Trust me they will become very beneficial in your carrier life when in meetings or giving references on inquiries.