Generally speaking, outside of CNY, there’s no benefit to advanced booking online (except in Thailand, H.K. and the Philippines) in terms of saving money, and you’re right, many many times you get a break from the rack rates coming in off the street. Note I said outside of CNY. If you were going to mainland China I would say fuck it completely and just roll up. However, during CNY, it might be to your advantage to try and book something in advance so you don’t wind up wobbling all over Tainan looking for a place to crash. This is debatable and I’m disappointed that no other Forumosan has weighed in. I would say that this is not a question that comes up every day. Anyway…there are loads of budget accommodation in most, if not all of the areas you plan to visit. It has been my experience that the hotels in the big cities are more or less half-full during CNY, and that includes Taipei. I had no problem finding nice lodgings in Kaohsiung and Penghu during the days leading up to CNY 2010. Same for H.K., Guangzhou, Xiamen, et al but you’re not going to China.
Here’s something you didn’t mention: How’s your Chinese? If you said “Non-existent” or anything similar, expect some obstacles, especially in the hotel and transportation category. Food is easy. Point, pay and eat. It sounds like you know what your doing already. Just curious. I got mercilessly fucked my first go-round in the mainland for not being able to speak intelligible Mandarin. I wound up on buses going to places I didn’t want to visit, showering in cold-ass water, asking for domestic dog meat, and ordering 8 beers that came to my table at the same time (because I didn’t understand the Y100 minimum purchase scam).
In terms of its size, I would rate LP Taiwan worth its weigh in China White heroin. I see you have a back-up plan but whatcha gonna do if you don’t have internet access, which, in the sticks of Taiwan, may be a Quixotic experience trying to wire up? I don’t care if I’m making a day trip to Keelung or Fulong, I put it in the sack and sweat the extra calories just in case. That’s me.
Looking again at your itinerary, I notice that you’re really moving around on the 3rd and 4th. I’d re-think that but again, that’s me. The HSR will be running but look out for two things: (1) Taxi drivers not using the meter and charging special CNY price from Zuoying to Kaohsiung City and (2) the fact that a healthy chunk of Taiwan is going to be moving around during those times. In other words, get online and see if there are any HSR tickets from Tainan to Kaohsiung to Taipei still available. You can always take the regular train or a bus but IMHO, you’re making a big mistake. thsrc.com.tw/en/
It occurred to me that perhaps you may be a little more of a free-wheeling traveler, e.g. prefer not to plan ahead. I like to have a landing pad at the beginning of a trip. For instance, when making extended journeys (more so in China) I typically book a hotel room online for the first and last night. Therefore, if it were me, I’d have booked my first night in Taichung and my last night in Taipei.