Hello there, does anyone know a quiet cafe (no loud pop music playing) with tables to work at and fast internet in the center of town or in the north (Beichen)? I know in Kunming "fast internet" is relative, but still... Thanks for any advice...

Burger King next to Metro is quiet off peak. Outside of meal times, most fast food places are quiet. The coffee is OK too, and no loud music.

For places with power outlets, try the cafes/restaurants on the eastern part of the Beichen pedestrian street. Tessi Toss is normally quiet the whole day.
There's also a new place next to the Pizza Hut near Carnival Mall called Zoo Coffee. It's not particularly quiet, but there are few people during daytime and they have a 50mb connection. Best part is that they are strict about not smoking inside. They have tasty food too.