The Apple store on Bade is being renovated. Not sure whether or not they’ve moved. Anyone know? If so, where to? I’ve got a failing external hard drive to return.
Edit: Tracked them down by searching for their address and finding the phone number. They’re now located at Zhongxiao Dunhua, MRT Exit 6.
I went by there this weekend to have my iPod repaired and noticed that they had moved too! I’m not super familiar with Taipei (I live in Hsinchu)… do you have the actual address by chance? Or is just outside Exit 6? Thanks so much! 
Just a side note. The store at exit 6 has been around for a few years.
Another note:
There is a less known Apple store at the computer market. Its actually on the North parallel Civic Boulevard (North, East of the main building). That’s where I was advised by the local computer geeks in that area to get one as they throw in a lot more software with purchases. I wasn’t disappointed at all. Of course they always give you the “We cannot offer illegal software on any of our purchases” line. And of course I paid full price for all of mine, as I would never dream of using pirated software. Seventy percent of which I have no idea what it does. 
Awesome, I’ll check it out. Thanks!
The Apple store on Bade has reopened. They extensively remodeled the space.