Jhushan
The top attraction in Alishan, everybody crowds aboard the predawn trains for the half-hour trip to this peak on the east side of Alishan, where you can see the sun rise over Yushan. There's a viewing platform right next to the station, but it's worth it to hike an extra 15-20 minutes past the helicopter pad to the very top, where the crowds are a little thinner. As the sun is already up behind the mountain, the sky is already quite light by the time you get to the top, and the sun is very bright when rising up -- hawkers sell disposable $10 eclipse-style filtered glasses, but it's better to not stare at all. On the way back, skip the train and walk back instead, it's a pleasant 3-4 km downhill hike.
Two Sisters Pond
Two scenic little ponds in the forest. The Elder Sister Pond, the larger of the two, has a much-photographed octagonal little pavilion in the middle. The demanding trail to Tashan starts from here.
Sights around Alishan are signposted in Chinese, English and Japanese, and as you walk around the trails you'll find that nearly every tree of size, age or unusual shape has been dubbed with a fanciful moniker like "Elephant Trunk" or "Three Generation Tree".
Shoujhen Temple
The largest temple in Alishan and definitely worth a visit. The exterior and first floor are imposing enough, but don't miss a visit to the second floor, featuring an incredibly ornate golden altar and a surreal room with 10,000 miniature Buddhas, each lit up with its own LED.
Giant Trees Trail
There are in fact two of these, both near Shermuh station, and they can be walked in a pleasant half-hour loop. True to the name, the cypresses here are giant indeed, and many have been growing for well over a millennium. The small Cihyun Temple, originally built by the Japanese, and the Tree Spirit Pagoda are along the way. The trail is particularly spooky when the mist rolls in.