I'm going to try a new apartment when I visit BKK in 2 weeks time. Its "Silom Convent Garden"
www.silomconventgarden.com in Soi Pipat, I think next door to Sauna Mania.
They have weekly rates from 10,000 bht for studio rooms with free broadband. Looks good on wensite. Will let you guys know a verdict later.