The Hsinchu Foreigner Assistance Center offers free classes for foreigners. It's my impression that it's a tutoring set-up, with college interns doing the tutoring. I singed up, but I haven't started yet. It sounds promising, but like I said, I haven't started yet. I talked to them on the phone and they spoke English, and then sent me an email with more info.
Here's the contact info from the email:
(1) Address：Hsinchu Foreigner Assistance Center (No.107, ZhongYang Road, Hsinchu City 300, Taiwan)
(2) Tel.：03-5229525 or 03-5216121 #564、565