Most of the Starbucks in Bangkok have WiFi, a prepaid service offered by KSC. You can buy prepaid cards at Starbucks or any number of retail outlets. A twenty (20) hour card goes for 1,500 baht, although I was buying those for ~ 1,350 from a shop in the Fortune IT Mall.

There are open and free WiFi AP's around town, in malls, hotels, bars, office complexes, but finding them and getting AC power can be challenging. ( The Big Mango Bar has free WiFi.)

Khon Kaen will be a bit more challenging. When I do not have broadband or WiFi access, especially in Issan, I use GPRS. I have pre-paid mobile phone service from 1-2-Call, (DTAC and TrueMove also offer GPRS.), and they offer a lot of GPRS packages. I subscribe monthly for 25 hours for 107 baht (the 7 baht is VAT). I get full GPRS data rates (80 kbp/s) throughout Thailand. Essentially you are using your phone as a modem, and 1-2-Call as an ISP. You'll need a GPRS capable phone. If a 1-2-Call pre-paid subscriber just call 1175, press 2, and the CSR can help you set up GPRS. I use a Nokia handset and Nokia PC-Suite which offer One Touch Access (no configuration), but you can set up this type of connection as a dial-up conection. I believe the number is *99#, with no username or password (CPID serves that function).