Bring your US$ here, and exchange them when you arrive.
While foreigners complain about the banking system here, you will find that it’s fairly efficient when it comes to get rid of US$.
The exchange rates are fairly standard.
Also note that a fair amount of foreign exchange transactions go in and out of Taiwan as it’s a very big trading country. Therefore, the local banks are more than up to the task.
At least when remitting money in and out I have nary had an issue with the banks I have been in contact with, which include CHB, Hsinchu International Business Bank, Union Bank etc.
US$ can be exchanged in banks all over Taiwan, and you are not only limited to ICBC. They will display the exchange rates on an electronic board in the bank, and you can ask around and compare prices before exchanging.