Black Swan Pub
Sukhumvit Road, near soi 12, just under the Asoke BTS station.
Free wi-fi is now offered.
Serendipity Cafe
Sukhumvit Soi 11
It's the old teak building next to Cheap Charlies which also has accommodation. Reasonable speed.
Old German Beerhouse
Sukhumvit Soi 11.
More details about this venue can be found here.
http://www.old-german-beerhouse.com/
Dynasty Grande
Sukhumvit Soi 8.
This new hotel has free wi-fi available in the lobby. This signal may be picked up from some rooms - presumably those on the lower floors. A free LAN connection is provided in the rooms for those who cannot pick up the wi-fi signal from their room.
The Fun House
Sukhumvit Soi 11
At the end of Sukhumvit Soi 11, the Fun House is now offering customers free wi-fi service.
Stable Lodge
Sukhumvit Soi 8
Has free wi-fi available. They used to have a password, but gave up on that. Some of the rooms on the lower levels get a connection too. http://www.stablelodge.com/