Where did you like the most in Taiwan?
On Sun Moon Lake there are two main towns: Shuishe (Shuishe) and Ita Thao (there is a bit more civilization there).
We stayed in Grandma Yu's B&B in Shuishe (it's available on booking), on Google Maps it is called 游ㄚ嬤的鄰家民宿. (Your sister lives with the family next door)
There is a bus that goes around the lake, and you can rent bicycles everywhere (there are regular ones and electric ones).