I think the best place is major banks who are handling foreign currencies.
Here's the example of Mizuho Bank.
http://www.mizuhobank.co.jp/info/gaika_ryogae.html
Outline of foreign currency exchange
http://www.mizuhobank.co.jp/setsumeisho/pdf/gaika_ryogae.pdf
More details in pdf file
For currency exchange (between JP Yen and foreign currency), they do not charge any commission, just they apply the exchange rate.
TTM Rate (which is the fixed rate by Mizuho bank for the date based on the market rate which is changing constantly even during the same day as far as the market is open), and there're fixed "difference" between the buying rate and TTM or selling rate and TTM rate for each currency.
In case of US$, it is 3 Yen.
e.g. if the TTM for the day is JPY95/US$, buying rate is JPY92/$, and selling rate is JPY98/$.
For Taiwanese Dollar, it is JPY0.5/TWD.
When the TTM rate is JPY2.84/TWD, you can buy TWD at JPY3.34\TWD and when you want sell it, bank will buy it at JPY2.34/TWD.
Though the TTM rate and the rate charge may vary among the different banks, the difference should be quite small and negligible.
Lates Exchange Rate for major foreign currencies:
Bank of Tokyo Mitsubishi UFJ
http://www.bk.mufg.jp/gdocs/kinri/list_j/kinri/tvl_check.html
Mizuho Bank
http://www.mizuhobank.co.jp/corporate/bizinfo/information/market/cash.html
Sumitomo Mitsui Banking Corporation
外国為替相場 : 三井住友銀行