Coffee pirates is near the university of vienna so you'll have a bit of academic buzz as students file in to bang out classwork, so it's work friendly for sure. The seating is plentiful and comfortable enough but only some spots have access to plugs (i mostly sat in the front entrance area) and the little nook off to the side. The wifi is good. the coffee is good and they have a nice selection of cakes and other food if you get hungry. I really like coffee pirates, i've been here many times.
Furniture cafe (das mobel cafe) fills up with people working on their laptops, art, or other projects as the afternoon progresses (so it's work friendly but get there earlier). There's some areas with a plug, so scope one out. The wifi was always good. he coffee and food are decent, it's also close to the parks in city center whichf makes for a nice stroll.
Phil is a bookstore that doubles as a coffee shop with cozy couches. this place is pretty work friendly. If you can read a book you can work on a laptop. the wifi was good but not available on weekends. There's a cafe section of the store with little tables, the food and coffee and more than acceptable. there's a lot of plugs.
Werkzeugh is one of the quirkier spots in vienna. I think at some point it was owned by a hacker (it's got these terminal themed menus). It's got plugs and nice booth tables in the back. it's got decent wifi. It's got a weird tent hanging from the ceiling and a good outdoor seating area too. The coffee was fine. The food options are limited to two items. One was a samosa, the other currywurst -- both tasty enough but more in the "snack" category. It's also a bar so you can grab a drink to numb the neurons. I worked there a few times and they were work friendly.
Cafe burggasse has a lot of plugs hidden away in the back room. Coffee is ok. Wifi is decent.
Short break is a new looking little coffee joint. I've worked there multiple times, and had coffee with friends there. The coffee and pastries were acceptably average. There is ample seating and good access to plugs. The wifi was good. I like the table seats next to the windows as you get a nice view of the street. It's on the corner of one of these rare residential tree lined vienese streets (most do not have trees), which is kind of cool.