Shilin Night Market (aka Shihlin Night Market) is the largest night market in Taipei and also one of the most popular. Full of delicious street food, small hole in the wall restaurants, souvenirs, and clothes, it is a great destination to experience Taiwan's night market culture.

Background:
Shihlin Night market lies next to Jiantan MRT station, surrounded by Wenlin Road (文林路), Jihe Road (基河路), and small alleyways Xiaobei Street (小北街), and Xiaoxi Street (小西街), forming a giant triangle making it the biggest night market in Taipei City by area. 
Shihlin may have the most food stalls and restaurants of any night market in Taiwan, and is often regarded as the best or one of the favorite night markets in Taiwan by both locals and tourists alike.
The night market features multiple alleyways as well as an underground food court and underground parking garage. 
Located next to Mingchuan University, Soochow University, China Culture University, and Shih Chien University, it has a constant supply of hungry university students visiting every day.

Shilin Market was first established in 1909 near the Matzu Cicheng Temple, which now lies at the center of the night market. Before that is was a resting stop for cargo on the way to Dadaocheng. 
In 1998, Shilin Market was named as a historical monument. After that from 1999-2011, the market underwent multiple renovations, and relocated to a temporary structure near Jiantan MRT station, until renovations were completed in 2012.

Hours:
Around 4 PM until 12 Midnight, every day.

How to get there:
By MRT: Take the Red Line to Jiantan Station and then take exit 1 north out of the station. The night market is right across the road. 
By Scooter: Take Zhongshan North Road out of Taipei and wind around Yuanshan Hotel into Shilin. You can park on the right side of the road next to Jiantan Station. 
By Car: Take Zhongshan North Road out of Taipei and wind around Yuanshan Hotel into Shilin. There are many parking garages around the night market.

Map: Please see below:

The first time I heard of Neiwan old street was when I asked my Mioali native coworker what there is to do in Miaoli. She told me there was a fun place called Neiwan. It turns out, Neiwan isn't even in Miaoli, its in Hsinchu, but obviously it is one of the most popular places in north-central Taiwan. I am not an expert about this location, but I would like to share my experience here with the world.

History:

During the Japanese rule of Taiwan, Neiwan was mainly a lumber driven town, as well as other industries such as mining and mineral extraction. Many Japanese era buildings still remain in the city, such as the well preserved police station. The main ethnicity here is Hakka, and you can still find lots of traditional Hakka food in Neiwan like their famed Zongzi.

Some popular destinations for tourists are the Neiwan Theatre (内灣戲院）, built in 1950 and and now converted into a restaruant, as well as Neiwan Suspension bridge （pitcured above).

The Neiwan railway was started in 1944 by the ruling Japanese, but construction was interrupted by WWII. It was completed by the ROC government in 1951 to help transport mainly lumber and lime. Now it is used as a commuter train for the suburbs of Hsinchu as well as a destination for tourists.

How to get there:
By Train:
Get off at Zhudong station and then take the Neiwan Liujia line.
This takes about an hour from Hsinchu.

By Car:
From Taipei, take National Highway 3 to the Guanxi Exit and travel down provincial highway 3 to Neiwan.

Map: