This library is right outside of the Chatswood station and the area is full of Asian restaurants and big malls. There are plenty of tables and chairs around but during the day, most of the seats are taken by the local highschool students (edit - I realized it's exam week when I went). There are quite a few kids who are casually chatting but not in a loud manner. There is a glassed corner near the entrance where you would be slightly more comfortable taking calls. Also, if you need 100% privacy and quietness, they have one bookable phone booth. It is free for the library members but it would cost you $2.50 / 30 mins if you are not a member. You can talk to the staff to book a spot.
A very popular coffee shop in Williamsburg. I've tried going several times to work but it's always been full. If you want a seat, be sure to arrive early (ideally before 9). Also, be prepared to queue up for ordering. The coffee was very good, and the tea was nice, but the cup size was very small (not sure if they do water refills). There are some snacks as well.
The interior is spacious, bright, and has a nice vibe. Even though it fills up very quickly it never got noisy. Plenty of power outlets along the wall side seats, and the WiFi is very fast (180+ Mbps).
A great cafe near Kunyang MRT, just a short 10 minute walk from the station. Although this at first might feel more like a restaurant it is definitely very workable on a weekday. I would recommend coming here for brunch or lunch and trying some of the great dishes, then working the rest of the day. I particularly like the counter seats by the windows, which looked like a nice spot to sit and work from. The WiFi is good and there are lots of power outlets. The cafe feels bright and modern, but it was a little noisy at times (people talking and slightly too loud music).
There are several Dreamers Coffee locations in Taipei, but this one near Sun Yat-Sen Memorial Hall is my favorite. They open at 7 every day, so it's a great place to work in the mornings, especially since it usually gets very busy after lunch. Good natural light thanks to the large windows all around. The large worktable (with power outlets) is great to work from. There are also power outlets by all the smaller tables. The WiFi works for basic browsing, but it's not super fast. Cheap drinks, but tea selection is slightly lacking in my opinion.
I've known about PuiBui for a long time, but never visited before. It's conveniently located near Daan MRT station. The interior is quite basic, but it still feels comfortable and the environment was quiet, good for working. The drink selection is mostly coffee, but I did find a black tea on the menu. They also serve good lunch options, including thai style curry and sandwiches. The portion size was quite good and the price was decent, especially since you get a discount if you order food and a drink. They have a "hidden" room with 5 tables in the back that is non-talk only. You have to ask for it if you want to access to it.
Another great cafe near Nanjing Fuxing station. The interior is quite large and has a nice modern vibe. There are several seating areas, and one large worktable suitable for working with a group of people. Very fast WiFi, power outlets, and decent selection of food and drinks. I can definitely recommend trying the German pork sandwich with Sourdough bread.