I've had good experiences in Kreuzberg with the smaller, independent places - they're generally more relaxed than the big chains. There are a few cafés there that are explicitly set up for laptop workers, with decent WiFi and enough outlets. My tip: just check out a couple of spots around Kottbusser Str, you'll definitely find something there. The only thing that matters is that you actually buy a couple of things - don't just have a coffee in the morning and then sit there for 8 hours.
Prenzlauer Berg is even more relaxed, I'd say. The cafés there are basically made for this kind of thing, lots of them even have tables specifically for people with laptops. Just remember: when you walk in, ask quickly if it's okay to sit for a few hours - with decent cafés you'll never have a problem. And invest in a good espresso or cappuccino instead of just drinking water, it's only fair to the place anyway.
Generally, I'd say try the smaller, independent spots instead of chain coffee shops. The atmosphere is better, the people are nicer, and when you buy something, they don't feel taken advantage of if you sit there longer. Some cafés even have regulars who work there all day - that's a good sign that the place is cool with it.