We were in Taipei last month (and managed to hit Japan was well 
). This was my first time in Taiwan, and I gotta say I was really impressed by the food (even with the high expectations).
Yong He Soy Milk King
Egg rice roll and of course soy milk with fried you tiao - great cheap way to start one’s day
We went to Yeh Liu geo park and then our driver took us to a restaurant near the water. They had tanks of live seafood and fresh greens - we chose some tiger prawns and rock cod (IIRC) with some greens - really fresh and delicious
Then went out to a Hakka town an hour away and went to this restaurant with a much of Hakka food. I highly recommend it if you schlep out - had to take quick snaps since we were with family. A couple dishes with braised pork, some very nice orange chicken, lotus roots, and fern shoots. And the best damn version of mochi with peanuts I’ve ever had.
Some dried persimmons done in a modern Hakka style - ridiculous!
Raohe night market
Got the obligatory pepper bun and it was delicious! Also the spiral fries and ubiquitous golden lava buns
Shaved snow in Jiufen- this was a random place that we walked into, but it was the best shaved snow I’ve ever had - those taro balls have the toothsome texture and fragrance that Meet and Greet’s lack
Almond milk shaved snow - this was a chain
Sunny Hills They used dried fresh pineapples without any winter melon filler
Formosa This classical Taiwanese restaurant might have served the best meal we had on this leg of the trip -we went twice
Fern greens
Sautéed clams
Salt and pepper squid
Congee with I believe squash
Lotus roots
Three cup chicken (delish!!!)
More rice cake
The crab special
A Northern Chinese restaurant (need to dig up the name later)
Perhaps the best scallion pancake I’ve ever had -like a Chicago pan pizza
Some tasty-but-super-phallic-looking rolls
Tofu
Had a bunch more dishes but was with family so didn’t snap everything 
Some random noodle shop next to the electronics outpost - proof not all noodles in Taipei are superlative
Ningxia Night Market
Liu Yu Zai taro balls - these were meh and definitely not worth the wait for me
Dude blowtorching filet mignon cubes - grisly, but outstanding for $3
Durian King - dang this golden lava durian ball was so decadent if you like durian (I love the stuff)
Lin Dong Fan noodles outpost at the airport - even though this was airport food, the broth was ridiculous - light yet beefy and so complex
These last a lot longer than the pineapple cake, so I’ve been savoring them slowly.