These are a few places I really enjoy.
Toh A (I highly recommend)
Addiction aquatic
A cut steakhouse
Il mercato in tianmu
鬼金棒 Ramen
Taverna De Medici
好記但仔麵 (My favorite Taiwanese restaurant)
Mitusi cuisine M
Yellow lemon is pretty interesting, good for dates. Everything you see I pretty much edible
Le Blanc
Good steak and lobster and drinks.
Maru Taipei
https://m.facebook.com/MARUTaipei/
Listed in the Michelin guide. The sushi chefs pick the food they give you.
Samwan gardens Korean restaurant is my favorite and most authentic Korean place in Taipei that I tried. Great Korean BBQ and traditional dishes and side dishes with great kimchi.