Surprisingly, it is possible to take a weekend trip to Taiwan from Tokyo. My flight left at 9:30am from Haneda airport and it arrived at 12:21pm at Taipei Songshan Airport. My main purpose to fly to Taiwan was to visit Kokyu National Palace Museum. It’s always meaningful to learn historical arts at Museums, but I really enjoyed just seeing the exhibited art designs, textiles and colors. Earlier is better to visit due to its popularity with tourists. It’s strongly recommended to visit Kokyu National Palace Museum around 8:30 am.
I only had 24 hours to spend, but it was heartwarming with Taiwanese welcoming atmosphere. If you too find yourself in Taiwan for a short amount of time, here’s how to make the most of a 24 hour trip. 
Wander the City
After checking into the PALAIS de CHINE HOTEL, I walked around Taipei Station. Near Taipei Station, 迪化街 (Dihua Street) there is a mixture of both modern and nostalgic atmosphere. It was right before spring festival, Chinese New Year, so the street was packed with people walking at slow pace. But, it was fun to see Taiwanese people and stores that were selling seasonal goods.
Eat: Noodles
If you get tired of crowds, you can escape to narrow roads where you will encounter much calmer scenes. I found a noodle shop with lots of local people at 16:00. The owner, who was the father, cooked noodles and his daughter took orders from tourists in English. There were many kinds of noodles and soups, so I just ordered the same as those who had ordered before me. This is always a safe and reliable way to order food.
Eat: Fresh Fruit
After a long walk, I rested with fruit juices at 豐味果品 which has a long history as a fruit shop with a sophisticated atmosphere, like a florist.
Eat: Dim Sum
For dinner, I went to 鼎泰豊 (Din Tai Fung) to eat 小籠包 xiaolongbao (eastern Chinese steamed buns). There are many cooks who create soup dumplings at tremendous speed. Mine was a crab soup dumpling with crab’s mark.
My recommendation is to try grilled dumplings, though. My friend’s daughter from the U.S. was so impressed with grilled dumplings that she ordered a second serve of grilled dumplings. I totally agreed with her.
View the Mountain Island
Taiwan has more than 200 peaks with heights over 3,000 meters. In Japan, we only have 21 peaks over 3,000 meters. You can see such mountain country from Kokyu National Palace Museum too. 
Walk in the Garden of Chian Kai-Shek
Near Kokyu, there was a 蒋介石 (Chiang Kai-Shek)’s house. His house and garden were so simple and practical, but very cozy. The garden was separated into several areas with various kinds of plants. My favorite one was the rose garden.
Enjoy Aozora open-air Market
After a heavy dinner the previous night, I preferred to eat some vegetables, so I decided to go to 四四南村簡単市集 Aozora open-air Market.
I miss Taiwan. I have lived and work there in my early twenties. Glad to see this post.
Thank you! Such a lovely country. I had a heartwarming experience there too.