The center of al furniture stores/factories is in Wugu. There you can browse to your heart's content, and if still not enough, then order custom made.
Then there are other options around Taipei. Heping West Road for example has a large, economical to high end selection of stores. I found my European made mattress there.
Xindian also has large furniture warehouses around Carrefour, a la Neihu. We used to have more, but the ones still remaing -on Baozhong road- have direct links to factories and are open to negotiations.
BTW, IKEA has had problems with furniture and formaldehyde before.