Travel in Taiwan is much different for me than when I lived in the Mainland mostly because I have a car here and I am married to a Taiwanese citizen (where I was single when I lived in the Mainland and often traveled alone.) If you want to take a train in Taiwan, you can. The island is small enough that you can get anywhere within a day on the train, though you have to go around the imposing mountain range that runs through the center of the island to go from the east coast to the west (or vice versa).
The territory under the control of Taiwan is divided into five administrative units. The largest of them is Taiwan Province. This includes the island of Taiwan (except for the two largest cities) as well as the Penghu Islands, Diaoyutai Islands (Senkaku Islands), and other smaller islands off the coast. Two others are the cities of Taibei (Taipei) and Gaoxiong (Kaohsiung). They have a status similiar to Beijing, Shanghai, Tianjin, and Chongqing in China. The other two are the islands under the control of Taiwan that are formally part of the Chinese provinces of Fujian and Guangdong.
As the island of Taiwan itself, it if further divided into counties and cities. Many cities in Taiwan are part of the counties that surround them, but most of the larger cities are not. An example is Taichung City. It is surrounded by Taichung County, but it is not a part of the county. It can be rather confusing to a first time visitor to Taiwan.
What is even more confusing is the rather confusing system (or lack thereof) of pinyin (Romanization) used on the island. There are four different systems of pinyin used on the island. The first is the old Wade-Giles System. There is at least one thing that all of the powers that be on this island agree on. That is that this is a HORRIBLE system of pinyin. This system is being phased out. The second is called Tongyong. This is a locally devised system of pinyin. It is clearly better than the Wade-Giles System, but there are still some areas where logic seems be in glaring absense. This is the system supported by the ruling Democratic Progressive Party. Third is the Hanyu Pinyin system. This is the system devised on the Mainland a few decades ago and is considered standard around the world. Even in Taiwan, most textbooks designed for foreigners as well as the language schools in Taiwan use this system. You will see very few public signs using this system, but it is legal for use by people on the island. The fourth is affectionally known by Chinese speaking ex-pats as suibian pinyin. Suibian roughly translates as 'as you wish'. I have seen all kinds of suibian all over the island. It is a wonder that ex-pats who can't read Chinese characters can get around at all. It is not uncommon for me to drive a couple hundred meters and see the same location rendered with three different spellings in pinyin.
Considerably more traditional Chinese culture has survived here than in China. While China is trying to repair the damage of the Cultural Revolution, it is doubtful if culturally it will ever recover, Taiwan has retained many elements of its traditional culture, and it can be seen all over the island. At the same time, Taiwan has a reasonably modern economy and one of the highest standards of living in Asia. You will also find many hospitable people whereever you go on the island. If you can get away from the cities, you will see breathtaking scenery and understand what brought the Portuguese to call the island Formosa (Beautiful Island).
I have traveled to a few wonderful places already. Over the coming months, I will create pages with pictures of some of the places I have been. Keep checking on my progress. If you have any suggestions, please email me.