Where in Taipei can I find a casual tea shop with a decent atmosphere where I can get a pot of tea / tisane?
Responses sooner than later are appreciated, as I need to go there this afternoon 
Taipei is a big city with a great number of tea houses. Did you have an area in mind or type of tea?
A popular though not inexpensive choice is Wistaria.
Or if you’re looking for something Western there’s the Rose House chain – again, not especially cheap.
For something for less money, just look around your neighborhood.
Taiwan Tea House’s variety is my favorite.