here's the VISA credit/debit exchange rate.
http://www.corporate.visa.com/pd/consum ... _rates.jsp
just add your bank % fees to get what rate you are getting. ALL VISA credit/debit cards will use the same exchange rate, only diff is your bank's % fees they charge you. you can withdraw cash at any ATM worldwide with the VISA sign but do check with your bank if there's any surcharge on top of the % fees for withdrawing cash.
the best way to get local currency in singapore is to bring your cash and get it exchange in the money changer. if you are exchanging a lot, you can haggle with the money changer to get a better rate. not all money changer rates are the same, so do shop around.
but for long term exchange, you will need to use a money broker which will do the exchange for you and do an electronic transfer into your local bank in singapore. their rate and fees are usually better than local banks (both in US and singapore) but it is still worth asking your US banks what are their fees and rate if you were to open a same bank in singapore.