This is an adjusted response I wrote to a question that showed up on the Taiwan subreddit. The usual question for visitors is if they can rent scooters with an international drivers license.
While bringing the license from home does give you the legal right to drive as a visitor in Taiwan for up to 3 months, you'll have a hard time renting a scooter anywhere in Taiwan with it. With limited exceptions, local renters only take local licenses. Only in Kenting or Hualian will you find someone willing to rent you a scooter without a local permit, and it's usually a matter of walking to every store in town until one says yes. If you go with a local friend, all things will go super smoothly because they have a local ID. If you go alone, or with another group of foreign tourists you'll end up paying modestly boosted prices and likely get a trashier machine. The fact that you have an IDL in your hands will mean nothing to anyone. Expect to pay between 400 and 500 NTD a day. A few stores will say you can only do 200km a day or something similar without paying more. Unless you plan to drive around the whole country you won't go over the limit. The only time your IDL is going to help you is when talking to the police in the event you get pulled over or into an accident. The way the law and procedure tend to work you'll likely get treated as an unlicensed driver in the follow up to the accident anyway, so an IDL only serves to save you from the driving without a license ticket.
A notable exception to the "no one takes IDLs" thing is car rental agencies. There are a few of the major car rental chains are around in Taiwan, but they only trade in cars. A car can be a great way to travel around Taiwan however, it's just a terrible choice for city driving. If you're looking to do a trip where you travel between cities, east and west coast and into the high mountains a car is an amazingly smart choice. In Taipei you won't need a scooter thanks to the MRT system, buses, and bike share programs. Most of the winter months are quite rainy anyway, and it can be quite chilly riding on a scooter, so you're not really missing much there. The roads are quite slick in places - anything with paint on it, for example - and if you're not used to the driving style you're more likely to get into an accident, held liable for damages, etc., even if you have the proper paper work.
You can do nearly everything famous in Tainan on foot if you plan things correctly and make sparse use of taxis, but there is a new bus system there and you can find pedal bikes available for rent for far cheaper than scooters. Taichung is more comfortable by car than anything else, but public transit can be combined with taxis if you budget your time right and stay int he city. Kaohsiung has an MRT system that works reasonably well, but driving is generally far faster and preferred by the locals.
The only place you'll genuinely want to rent a scooter is on the east coast or down in Kenting. Traffic in these areas is also much much lighter, and if you're not used to driving in Taiwan it's a good idea not to get in over your head. I wrote an article for on-road safety for bikers but its equally applicable for scooters in almost every sense.
Here's my best practical advice for renting a scooter during your time in Taiwan. Get a local license when you get here and skip the IDL all together. There is a written test, in English, at the DMV for a 50cc scooter, and a simple driving test - if you know how to drive a scooter - to get up to 150cc. Now you can rent scooters without an issue anywhere and you're covered by the minimal insurance policy it has! If you skip having any license, including an IDL, and drive you're breaking the law and you're going to have to deal with the consequences should they arise. Just to repeat that driving without a license is super illegal even if a store does rent a bike to you. What you need to consider is for the time you'll be on a scooter - a day, or two? - the hazy legality of IDLs in post-accident insurance/legal proceedings, it's main benefit being no ticket for no license, is it worth the hassle of getting a motorcycle stamp back home. The next thing to consider is it worth renting the scooter at all?
Best wishes for a fun ride, and remember to wear your helmet and bring a rain coat in the trunk of your bike. If you're going to rent in Kenting, as stupid as it sounds, bring a super light long sleeve shirt and gloves to keep yourself covered. Mega sunburn really, really sucks.