actually, if you want to catch the sunrise in Alishan (which is wat most people do), get to Alishan itself the day before. You can either take a train up or a bus. There are many hotels there. But if you are on your own and don't want to spend too much money, there are some small guest houses there. Some are just above the shops or restuarants. Walk around and ask. There is no need to book in advance unless you are going there during peak period eg Xmas/New Year or local public holidays. In the mornings, the hotel people will wake you up at 4 plus, you head to the train station with hundreds of other tourists and take a train to the top of the mountain and wait for the sunrise. It is a long wait, but is worth it. sunrise itself is over within 15 min. And everybody will rush for the returning train. Within half an hour, the whole place will be empty and you can have the whole mountain to yourself.
there are oso some treks around the area. if you like being with nature, can wander around the whole area for half a day or more. very tranquil.