There are zero airlines offering flights to Taipei. The most direct route isn’t necessarily the cheapest – being flexible is key to finding the lowest airfare rates. For example, try searching by month to see the best time of the week to fly.
Make sure you use the search options above to search for flights to other airports in Taipei, not just Taipei Taiwan Taoyuan International (Chiang Kai Shek International) Airport. The more options you look at, the better your chance of finding a cheap deal.
You can expect accommodation prices to be higher at this time of year too. Last-minute deals do crop up, but it's best to book everything in advance to avoid disappointment.