In Tainan I can recommend the Cheng Guang Hotel (成光別管）. It's at 294 Beimen Road, a short walk from the train station. Single rooms are just NT$600. Nothing fancy but there is nothing you can complain about at that price.

You might try the tourist information line 0800 011765. The Lonely Planet and Rough Guide often have info on budget accommodation if you can get hold of them (or take a quick peep at the bookshop). Wikitravel (a sister site of wikipedia) might have something. www.ask.com gives answers to questions in direct English such as "where can I find cheap accommodation in...?" Hope this helps. Cheers

I would actually suggest against both Cheng Kuang and the one opposite to it GuangHua hotels. For this price, there is something to complain about.

After spending two horrible nights in those, I finally found a better, much bigger and a bit cheaper option just across the square from the Tainan Train station to the west. The tall building across the street from the expensive Tainan hotel has some very cheap and convenient options on the 11-13th floors. The TV channels offered suggest that some Taiwanese use it for more than just travel, but it's affordable, spacy and very clean.

Either way, there's also a list of some options here : http://www.eslisland.com/life/Tainan-Hostels-Hotels.htm