The unit of currency for Taiwan is New Taiwan Dollar (NT$).
There are 5 denominations for Paper Notes and 5 denomination for Coins.
For Paper Notes it come with NT$2000/1000/500/200/100 denomination.
For Coins it come with NT$50/20/10/5/1 denomination.

Foreign currencies can be exchanged at Government-designated Banks, Departmental Mall and Hotels. Bank of Taiwan have setup a 24 hour Money Exchange in Terminal 1 and 2 of Taoyuan Airport.

Here’s the list of Bank in Taipei

Taipei Fubon BankNo.50, Sec. 2, Zhongshan N. Rd., Taipei City+886-2-2542-5656
Chunghwa Post Co., Ltd.No.55, Sec. 2, Jinshan S. Rd., Da’an Dist., Taipei City+886-2-2321-4311
SinoPac Bank


No.36, Sec. 3, Nanjing E. Rd., Taipei City+886-2-2506-3333
Taiwan Cooperative BankNo.77, Guanqian Rd., Taipei City+886-2-2311-8811
First BankNo.30, Sec. 1, Chongqing S. Rd., Taipei City+886-2-2348-1111
Chang Hwa BankNo.27, Sec. 1, Chongqing S. Rd., Taipei City+886-2-2361-7211
Hua Nan BankNo.38, Sec. 1, Chongqing S. Rd., Taipei City+886-2-2371-3111
Cathay United BankNo.65, Guanqian Rd., Taipei City+886-2-2312-5555
The Shanghai Commercial & Savings Bank, Ltd.No.2, Sec. 1, Minquan E. Rd., Taipei City+886-2-2581-7111
Mega International Commercial BankNo.123, Sec. 2, Zhongxiao E. Rd., Taipei City+886-2-2563-3156
Bank of TaiwanNo.120, Sec. 1, Chongqing S. Rd., Taipei City+886-2-2349-3456
Mizuho Corporate Bank8F, No.68, Sec. 5, Zhongxiao E. Rd., Xinyi Dist., Taipei City+886-2-8726-3000
CitiBank1F., No.74, Sec. 3, Mincyuan E. Rd., Jhongshan District, Taipei City+886-2-2503-0077
DBS BankNo. 85-1, Sec. 1, Zhongxiao E. Road, Jhongjheng District, Taipei City+886-2-6612-8311