Goverdartsi is not exactly a thriving hub of alternative attractions for international skiers.
If you are looking for more than ski lifts and nature (lots of nature) you should think about heading to the pretty spa town of Sapereva Banya for a dip in their piping hot mineral waters, the Rila Monastery for it's stunning architecture and UNESCO accreditation or even Sofia to get a taste of the "big smoke" and it's own ski resort, Vitosha.
Borovets of course has a few more tourist attractions so may also be worth visiting if you are planning a big night out or fancy a change in diet.