Alishan is famous for High Mountain Oolong (高山烏龍 Gau-shan wulong) tea and you'll see plenty of plantations on the way up. There are a number of tea shops in the main village that will serve up a pot the traditional way for $200 or so. They will also let you try a number of teas for sale, and this is a good way to pass the evening. But this is with the expectation that you will buy something. Teas are mostly sold in vacuum sealed bags of 150g, and usually will cost between $400-$800, although some can be as high as $3000 for this amount.
Nightlife in any sense is virtually nonexistent, but all restaurants are happy to sell you a beer and you can pick your own poison at the convenience stores.