I'll try to be polite.
Recent trips to Puli and Alishan have reminded me that the point of those places is as a base to areas nearby, not to them.
Puli is just another dull town (I await a defense of it) with lots of great mountains, rivers etc nearby. Ensure you have transport to get you out of the urban area.
Alishan is fine if you've grown up hearing about its wonders. For more outdoorsy types it's essential to get away from the main zone. I strongly recommend Tatajia (watch out for the excellent grey leaflet published by the Nat. Park) within the boundary of Yushan National Park, and the villages Fenchihu, Taihe, Rueli (good colorful info from the Alishan Scenic area admin) etc further down the mountains.
Transport is as with many places in Taiwan problematic - without a scooter anyway. To get to Tatajai I suggest hitching (yes yes I know I shouldn't mention this...) the 20 something km from the Alishan entrance. For the villages down the mountain get off the small gauge train halfway up and walk!
Yushan closed After changing their minds several times the National Park decided to keep the main peak open without a 'rest' this year. The recent cold weather though has forced them to close the higher peaks in the last few days due to 'heavy' snow and ice.
