I don’t think there will ever be a complete business directory listing in English for Taiwan and probably not enough to sort them by cities. But anything is possible for the globalizing Taiwan. I sometimes use “Taiwan Yellow Pages”. Here is the Patent link: http://www.tw-online.com.tw/English/EAttr_Search.asp?cate=1122
I don’t know Chinese, so I can’t say the following with anything like complete confidence (that is, this might turn out to be one of the many times in my life when I have been mistaken about something):
There appears to be some kind of searchable list or database of Taiwan companies at this URL:
If you’re using the translation function on a Chrome browser, the first radio button on the line that begins with “The query” (“查詢條件”), the radio button labeled “Company Name (English),” is a mistranslation of “公司名稱(中文).” It should read “Company Name (Chinese).” The second radio button on that line is for foreign companies and apparently takes English input.
I got the above URL from the webpage pasted below, by clicking a link that says “公司及分公司基本資料查詢,” which Chrome translates as “Companies and subsidiaries query”:
Here’s a searchable list of patent attorneys in English (I’ve had trouble loading this page on at least one occasion; it loaded after I cleared my browsing history):
The list has drop-down menus that allow searching for patent agents, patent attorneys, or both, as well as searching by address. Choosing “address” seemed to work when I tried looking for agents or attorneys by merely pasting “Taichung” and “Kaohsiung” in Chinese (but I didn’t get anything with “Tainan”).