The Bicycle Tour of Taiwan is undoubtedly one of the most exciting things I have ever done and definitely in the Top 10 of my experiences in Taiwan. You have to do it! Provided of course that you are fit enough! It is a 1,000-kilometer ride. Mostly flat, except when you cross from West to East in the South and from Hualien to Su'ao. I said 'when you cross from West to East' and not 'from East to West', you would have noticed. There is a simple reason to this: the most difficult and stressful part of the ride lies 10 kilometers north of Taroko (the national park near Hualien). If you cycled around clockwise, you would reach that tricky spot only after several hours of slopes, even if you departed from Su'ao. But if you cycle counter-clockwise, you will reach that tricky spot after only one or two hours of flat roads, which will be much easier for you. I know what I am talking about, I have cycled around Taiwan three times.
I suggest you buying a good bike and start from wherever you are. I have only lived in Taipei and in Toucheng (Ilan county), so I can talk only about those, but please start from wherever you happen to live right now. I advise you to do it in the summer months. Avoid May and June though, for these two are the rainiest months. In other words: July, August, September or October. I have done it in February once. It was much sadder than during the high season. You won't believe me, but I met only another guy who was doing it! If you do it in the summer, you will see hundreds of other people on the roads.
Most people take between one week and two weeks to complete the tour. I advise you to take your time. For my part, I did it twice in 8 days and once in 9 days. If I had to do it again, I would take 10 days, in order to sip Taiwanese life and Life itself, or at least my own life, a little bit more. If your time in Taiwan is counted and if your are an athlete, know that you could easily do it in 7 days. I think that if you start the tour from Taipei you might either depart from your own place or from the 101. The first day isn't the most pleasant. You will have to cycle across Taoyuan county, which is probably the most polluted and ugliest part of the trip. Keep heart, the best is yet to come! When you are tired, ride towards the nearest town and look or ask for a hotel. My first time it was in Danshui (I had begun in Toucheng), my second time it was in Changhua and my third time in Taichung. But you could decide to stop in Miaoli, for example. It isn't good to get exhausted on your first day. The second day will bring you more delightful landscapes. You should head towards Chiayi. On the third day, you can either cycle towards Tainan or, if your legs are fine, towards Kaoshiung. Tainan is a pretty city. I advise you to stay there for a night. If you look for a bigger and more modern city, and once again if you aren't too tired, head towards Kaoshiung.
On your fourth day, head either towards Pingtung (from Tainan), to Kenting or to Taitung. If you have never been to Kenting before, I warmly recommend it to you. In Kenting, you could take a day of rest or even two, since it is a very pleasant town, in front of the sea, with good food, good music and breath-taking sights. On the next day, you will go to Taitung, if you haven't reached it yet. Here, you will encounter the first serious slopes. Don't give up! The East side is the best! The Pacific Ocean is here, awesome! This side is so beautiful that some people actually skip the West side and only cycle here! Many others do only one chunk: Taitung-Hualien. That's what you will be doing on the following day!
If you intend to do it in one day, you will have to wake up before the sunset, because this is a 200-kilometer ride and you can't afford to ride at night here: there aren't any road lights once you are outside of town. The following day, Hualian to Toucheng or any town in Ilan county (Ilan, Luodong,...) is a special day. How can I put it? Shall I tell you? It's all at once the most beautiful, the most physically challenging and the most dangerous chunk. Those who haven't done it can't understand what I am talking about. It's not a day you will forget easily. There are 12 tunnels to cross. It's not for the faint-of-heart. If you are a woman, a group or a not-too-adventurous person, I advise you to take the train with your bicycle from Hualien to Su'ao. A last thing about this part... You may puncture because the roads are full of pebbles and metallic things fallen from the numerous trucks passing by.
The following day, Ilan to Keelung: this is the most enchanting day. You still have this stupendous Pacific view on your right side and the gorgeous mountains and hills on your left side, but this time without slopes, so to say, and with towns and convenient stores much more often. The last part, from Keelung to Danshui and then from Danshui to the city center is also a great experience. Taipei has 111 kilometers of bikeway: you won't have to ride much with the cars. It's mainly flat again. You will see Baishawan and several other white-sand beaches. Gorgeous places as well! You will be tired, but happy, having seen hundreds of stunning places and hopefully having met dozens of friendly and open-hearted Taiwanese men and women.