you need a tripod when you can no longer take the photos (assuming that you want them sharp) with a shutter speed where handholding will give you a sharp result.
whether it is necessary, how would i know? of course there will be times of the day in taiwan where this comes into play, e.g. night time is a good example. some people prefer to just walk around without tripod and shoot high iso, some people don't mind bringing it along to shoot low iso, long shutter speed night scene..... it depends on your preference. no point buying it if you're not going to use it.
A very good but not-so-famous photographer once said, "If no tripod, how to take landscape photos?". Yes it sounds extreme, and it may due to the crude translation from this "没有三脚架,拍什么风景照?!". And if you take some low light landscape photos, a tripod is worth its weight in gold, and is many many more times more important that a good lens.
Anyways, I wouldn't bring it if the people I'm traveling with will not be patient with me when I set up my tripod (I'm slow) etc. I would just shoot with my 35mm f/1.4 at ISO 3200 or higher which allows me to have sharp photos in low light situations at 1/30s or faster shutter speeds.
We don't know what you want to shoot, how you want to shoot, what else you're bringing and how much time you want to spend shooting.
Personally for my coming holiday, I'll be needing a tripod cos I'll be shooting stair trails (hopefully) which can not be done without a tripod.
Many things however, like landscape shots, shots in low-light and even panoramas are possible without the use of tripod.