There are a bunch of cafes in the Gongguan area with free wireless. For ex - Norwegian Wood and Kafka on the Shore (both are located on the block immediately to the left of the Taipower Building). Near Shida are even more cafes, including another location of Bastille, and a cozy place called Morelax. They let you linger for a long time, have a wall of books/magazines, play pretty good music (chosen by their scruffy waiters from essentially the cafes’ private CD collections; no canned Starbucks Christmas carol crap), and on occasion sponsor artsy events (poetry readings, acoustic guitar shows, etc). However, be warned: the coffee in these cafes is pricey – avg $120 (which is actually only about $10 more than a Starbucks latte).