In Taiwan, you can get around very easily. Convenient modes of transport are all easily available. There is the Metro, the railway network and air travel. Apart from that, you can also get around by bus and cab/car.
The primary domestic carrier of Taiwan is UNI Air. The flight frequency is quite good, so there aren't long gaps of waiting. Taipei and Kaohsiung offer the most regular and smooth services.
Taiwan has two major railway networks - the Taiwan High Speed Rail and the Taiwan Railway Administration. The former is more generally preferred and the stations and platforms they halt at are all wheelchair friendly.
Taiwan's bus network is quite extensive. Private companies offer a lot of buses. Intercity buses are cheaper than even train travel here. Taxis are available in abundance. Finding or hailing one is no problem at all, as they're almost always waiting for passengers. These taxis are metered and you do not need to tip the drivers. You can also rent car, a scooter or a motorcycle to drive around the cities, provided all those vehicles are insured and registered.