From Taipei I took the HSR (high speed train) to Taichung and then the bus to Sun Moon Lake. I bought the ticket for the train in advance online and it costs TWD 700 while for the bus there's no need to book in advance and there is one every hour.
In SML I took a basic hotel, convenient to what I had in mind to do, that is renting the bike to go explore the lake and then to climb Mt. Shuishe. My hotel was in fact in front of the Giant shop that rents bicycles and next to the bus station of Shuishe.
My recommendation is to spend at least 1.5/2 days in Sun Moon Lake. One day you can rent the bike (really nice Giant shop on B1 of the Visitor Center building) and either do the full loop (around 30km) or just a few parts of that. In any case you have to stop and visit all the amazing temples along the way.
I did the full loop starting from Shuishe Visitor Center going clockwise and stopped at Wenwu Temple, Xuanzang Temple (Xuanguang is a smaller one next to it but it's nothing special) and the amazing Cien Pagoda with a breathtaking view!!!!
You'll also find many view points where to enjoy the peaceful and beautiful scenery.
Some more shots to show you how wonderful it is!
The other day you can do some hiking!
Mt. Maolan is a short (around 2km) and easy one, it starts behind Shuishe Visitor Center, while Mt. Shuisheda it's way more challenging and starts from Ita Thao.
This last one takes around 6 hours and it has around 800mt elevation. Make sure you have enough water and snacks with you because there's nothing along the way! The surrounding is amazing and very very wild but from the top there's not a great view since it's mainly covered by he trees!