The abbreviation of Taiwan Dollar is TWD or NTD.
The biggest number is 2000TWD. However, I suggest to exchange to 1000TWD because the most people are using is 1000.
The cheapest and most convenient way is to do exchange at the airport.
There are 2 banks at the airport which are Bank of Taiwan and Mega Bank. The rate is similar so you can do exchange in any of them.
To see above link, you will know the exchange fee is only 2%.
And you need to pay additional 100TWD per exchange.
Therefore, it is recommended to exchange your money to TWD once at the airport.