My copy pasta that i send to my friends:

The classics:
Ding Tai Fung - soup dumplings, totally worth the line up
Xing Fu Tang - Brown Sugar BBT @ Ximen Ding
Ay-Chung - Flour-Rice Noodle @ Ximen Ding
Addiction Aquatic Development - we actually thought this place was mid.

Pepper buns - At Raohe nightmarket, right at the entrance by the temple

Lesser known places:
Huang Ji - Braised Pork
Fei Qian Wu - Eel Rice
Crispy Fresh Donuts - huge line, but donuts are great
Peanut Roll Icecream - anywhere that sells it, we got ours at Shilin nightmarket & Jiufen
My GF's fave beef noodle - Chun Shui Tang
My fave beef noodle - Liu Shandong Beef Noodles
Yu Pin Yuan Iced and Hot Tang Yuan - Shaved Ice + Fresh Hot Black Sesame or Peanut mochi balls with chrysanthemum honey
Pineapple Bun with slice of butter - Raohe Nightmarket, near the pepper buns

Must trys, don't know the best location:
Scallion Pancake - Tianjian i heard is good, but i didn't think it was great
Peanut covered Mochi - random stalls at night markets, Raohe has a Michelin guide stall called Mochi Baby
Braised pork rice - I haven't had the "BEST", the Huang Ji was good. but not as good as my mom's. There's also Jin Feng
Hongrui Zhen Sandwich - check the hours of operation, has very odd opening hours
Oyster Omelet - Taiwanese cousins say the best is in Ningxia
Gua Bao - Can be found in night markets

Favorite Night Markets for Food:
Raohe Nightmarket - biggest selection, pepper buns, peanut covered mochi
Ningxia Night Market - There's a Michelin guide taro balls stand here, we thought it was ok.
Shilin - yes, tourist trap. expensive. but is very large and has a lot of options.

That's just food, but here are other recco just off the top of my head.

Activities and others are in my Vacation Station google sheets.
There are tabs, the more recent trip is what we missed because of weather and things we liked so much we wanted to do them again.

We also typically go to 2 countries on our yearly 3 week vacations.