Stickman has a pretty comprehensive list of free wifi spots around Bangkok, complete with short description of where they are and how good the service is. Given so many people travel with their laptops these days, it’s useful info. If you want a guaranteed broadband connection for your notebook, I recommend Asia Internet in the Times Square mall, right by Asok BTS. They have wifi and hotdesks where you can connect your laptop, plus a cafe doing cheap coffee and friendly, helpful staff. At one baht an hour it’s not the cheapest connection but it is speedy and it’s a pleasant environment to work in.
More on Bangkok wifi:
Spike | Google | Amazon UK | Amazon US | Wikipedia
Internet on Koh Phi Phi or Koh Lanta (where I am right now) is 2 baht per minute, so 1 baht per hour in Bangkok seems pretty reasonable really!