One day in Taipei
Get plenty of sleep for this jam-packed day. Expect to walk for this itinerary, so wear comfortable shoes, and dress for the climate. Due Taipei's hot and humid weather during the months of May to October, bring an umbrella in lieu of a raincoat if rain is in the forecast. Temperatures commonly hover around 35°C in the months of July and August, so unless you love saunas, avoid extended outdoor walks during those months.
Taiwan has the highest per capita density of convenience stores in the world. Drink enough fluids, but there is no need to bring a backpack full of food or drinks with you. Umbrellas, ponchos, spare underwear, alcoholic drinks, or anything else you could possibly need are for sale there. Just walk a few steps to buy something when you're thirsty!
The best way for first time visitors to get around is by the Taipei MRT or metered taxi. The MRT avoids traffic jams and is better for longer distances, while a taxi may be needed to reach a few destinations not within walking distance of an MRT stop. Taxi drivers are generally honest but often have a poor command of English - have your destination written down in Chinese if it is not particularly well known. You will get a discount on the MRT system by purchasing and using an Easy Card. Remember to return the card to get back your deposit (minus a small fee) at a MRT station before leaving the city.
Start your day early by eating a traditional northern Chinese breakfast. On your way out of the hotel, ask the concierge for suggestions. Yonghe Doujiang (永和豆漿) is a popular 24-hour outlet located throughout the city. Fuhang Doujiang (阜杭豆漿, Shandao Temple Station Exit 5) is a popular eatery, though the long line on weekends is not worth the wait. Although doujiang, shaobing, youtiao and other northern snacks do not originate from Taiwan, these mainland transplants were popularized in the Taipei suburb of Yonghe in the 1950s by refugees of the Chinese civil war who arrived in Taiwan in the late 1940s. The descendants of the 2 million refugees who arrived from Mainland China around 1949 make up only 13% of Taiwan's population, but over a third of the population of Taipei where they dominated the upper levels of government until the early 1990s.
After breakfast take a taxi or the MRT to Longshan Temple (Longshan Temple Station Exit 1), built in 1738 in traditional Fujianese style. You are now in the heart of what was once the Qing dynasty settlement of Bangka. In contrast to the hipper and glitzier districts further east, the working class residents of Taipei's oldest neighborhood regularly speak Taiwanese instead of Mandarin. The temple opens at 6AM. Go inside the temple and watch the locals pray for fortune and good health. Expect about 30 minutes to absorb the atmosphere and architecture. If you're feeling particularly religious, the incense is complementary.
Next, take a taxi or the MRT to the Chiang Kai-shek Memorial Hall (Chiang Kai-shek Memorial Hall Station Exit 5), which overlooks a central square flanked by the National Concert Hall and the National Theatre. If you arrive early enough, you will see elderly people practicing taichi amid the picturesque stone paths and koi ponds of the grounds. The Memorial Hall opens at 9AM; expect to spend an hour there. Climb the stone steps to see the bronze statue of Chiang Kai-shek, flanked by two motionless guards. A changing of the guard ceremony occurs every hour (but if you plan to visit the National Martyrs Shrine later, feel free to skip the show for later). Descend the elevators to the ground level to view the exhibitions on Chiang's life, complete with his sedans and uniforms.
Ready for lunch? Exit through Memorial Hall's northern doors at the ground level and through dazhongmen onto Xinyi St., and take a taxi or either the 20 or 22 buses for a short ride over to Yongkang Street, famed for its collection of local eateries. If you're in a group of two or more, try the original Din Tai Fung （鼎泰豊) restaurant near the corner of Yongkang and Xinyi St., serving the best xiaolongbao (小籠包) the world has to offer (but you should arrive around opening at 10AM to avoid the wait). Or visit Gao Ji (高記) just around the corner for the same but without the crowds. Tu Hsiao Yueh (度小月) serves Tainan-style danzai noodles. On a side-street off Yongkang (Jinshan S. Rd. Lane 31) is Yongkang Beef Noodle Soup (永康牛肉麵), serving another mainland Chinese transplant that has become a staple of Taiwanese cuisine and perhaps the best option if you are alone. Remember to head to Yong Kang 15 for some shaved ice for dessert.
If you enjoyed the Chiang Kai-shek Memorial Hall, then take the MRT to Dazhi Station and transfer to a taxi or the 267 bus for a visit to the National Martyrs Shrine, which holds the memorial tablets of the war dead of the Republic of China. A changing of the guard cermony involving two sets of sentries occurs every hour when the memorial is open from 9AM to 5PM.
From the Martyrs Shrine, take a taxi to the National Palace Museum, which houses the most complete collection of Chinese art and artifacts in the world. The bulk of the museum's holdings were once housed in the Forbidden City in Beijing as the most prized possessions of the Chinese emperor. During the Chinese civil war, these items were brought to Taiwan under the orders of Chiang Kai-shek to keep them out of Communist hands. The collection is so expansive that only 1% is exhibited at any given time. Start from the 3rd Floor and works your way down, visiting the permanent exhibitions before visiting the special exhibits on the 1st Floor. Try to arrive by 3:30PM, so that you will have a good 3 hours before the museum closes at 6:30PM.
No visit to Taiwan will be complete without a visit to a night market. From the Palace Museum, take the 304 or S19 bus to the Shilin Night Market for a dinner of traditional Taiwanese snacks. The market has an indoor food court, as well as numerous food carts in the streets between the Jiantan MRT Station and the Shilin Temple. Try some oyster omelettes (蚵仔煎), ba-wan (肉圓), fried chicken steak (炸雞排), fried buns (生煎包), meat soup (肉羹), oyster vermicelli (蚵仔麵線), pearl milk tea (珍珠奶茶), or if you're adventurous, stinky tofu (臭豆腐). Remember not to get too much of the same thing so you can try different foods from different stalls. If you can't read the menu, just point to what others are eating. After dinner, head to the streets of the night market to shop clothes and other goodies.
If you still have some energy left, take the MRT to Ximending (Ximen Station Exit 6), the heart of Taipei's Japanese-influenced youth subculture. People watch the pedestrianized streets, which are particularly lively once high school students are let out in the evening but die down by around 10PM.
Taipei is a very safe city. Violent crime is nearly non-existent, but watch out for pick-pockets in crowded areas such as night markets. And beware of oncoming cars and scooters when crossing streets or walking around narrow, sidewalk-less side-streets.
When in need of help, just ask. The locals are extremely friendly, and almost all young people can communicate in basic English.