Where is Taiwanese Hokkien spoken in Taiwan and Asia
While it might be clear Taiwanese Hokkien is spoken in Taiwan, it's not spoken equally around the country. Generally speaking, Taiwanese Hokkien is spoken more in the south of Taiwan, in cities like Kaohsiung and Tainan compared to the north such as Taipei. While living in Taipei might not give you many opportunities to hear Hokkien spoken on the streets, Living in either of the southern cities, or more rural areas of Taiwan, you'll hear Hokkien much more often. Around the Taipei area, Taiwanese tends to be spoken a little more often when you go further into New Taipei City or around Keelung. Yilan is another area in North Taiwan which has a larger Hokkien-speaking population than the capital. From around Taichung and further south, Taiwanese starts to get much more commonly heard, especially in more rural areas of places like Changhua, Chiayi and Yunlin, where Taiwanese Hokkien can often be more commonly heard than Mandarin.
This map* gives a good idea of where Taiwanese is spoken more commonly within Taiwan. With data collected in 2010, it shows the percentage of those aged 6 or older who use Hokkien at home in Taiwan.
Taiwanese Hakka
Viewed more as the strongholds of Taiwanese Hakka, the cities of Taoyuan, Hsinchu and Miaoli also have slightly lower populations of Hokkien speakers. Here you'll sometimes hear Hakka spoken, especially out of the city centers. While Taiwanese Hokkien is still spoken around the area, Mandarin is more common there.Other variants of Hokkien
Apart from just Taiwan, Hokkien is spoken in many other countries too, mostly centered around Southeast Asia. Along with where Hokkien originated from in Fujian Province, China. Malaysia, Singapore, Philippines and Indonesia all have fairly large Hokkien-speaking communities, where Hoklo people migrated to. Each of these have nuances and some vocabulary that differs between them. For example the Hokkien spoken in Penang, Malaysia uses some different words and pronunciation such as words added from Malay that can make it a little difficult for speakers of Taiwanese Hokkien to understand at times. However they are still the same language and are generally mutually intelligible.
* Image taken from Wikipedia by user Kanguole. Licensed by CC.