wkkk, I know you're not Japanese but there is a popular Japanese owner hostel over there. Called Low Pressure Surf. You can pop around, I bet you will find people that you know from Japan. AFAIK there is 3-4 surf hostel there. All on the same street. Taitung Surf Shop(aka 5 Surf). Donghe Surf Hostel and Low Pressure surf. There's also now Screw hotel. I've never stayed at the 5 surf but I heard it isn't that clean compared to the hostels. However you would be glad to know that it has the best atmosphere and environment. On weekends when I walk pass it, I smell the Aboriginal BBQ that they have. All the drunk surfers and hot bikini girls sitting out there enjoying their BBQ.
Maybe Uncle Jaffa only met 5 fairies there but there are actually 8. Ba = Eight, Shien = Fairies and Dong = cave/hole
http://magicseaweed.com/Bashien-Dong-Surf-Guide/3450/You only get good waves on the right swell and then the rips are insane. I took one good look of it and how far the line up is and I gave up. Yes Jaffa is right, the waves is very good and for real hardcore surfers. It takes around an hour by car.
Make sure you rent a car while you're there. There's no public transport.
And of course not to forget, the best barrel in Taiwan is at Cheng Gong Harbour. Looking at the forecast, you might be lucky enough to surf there. Watch out for the sharp coral and reef. I would suggest to bring reef boots if you're going there.