I have 3 free days in my trip that I would like to spend in some mountain area in Zhejiang province.

Yandang is more famous and I personally prefer it, although it is further than Tiantai. From Shaoxing East Railway station, you can take a bullet train to Yandang Railway Station; duration is about 2 hours and ticket fare is CNY 110.5 for a second class seat and CNY 159 for a first class seat. Upon arrival, take the direct bus to the scenic area; or get there by a taxi at around CNY 15 (it's only about 3 miles away).