Just back from a trip to Singapore and Vietnam; I found that the best way is to withdraw Singapore Dollars from an ATM; from looking at the exchange places in hotels, side of streets etc, you were only getting at best 1.90$/€ while I was getting 2$/€ by ATM.
In Vietnam, I was amazed with the amount of people (non-Americans) who brought US$ with them as it is "easiest to use" in shops. That is nonsense, although a lot of local shops may accept US$, they will rip you off on the exchange rate; it is so easy to use the local currency, in this case the Dong which once you get your head around the exchange rate (26000Dong/€) is fine.
Six years since I was in Thailand, I brought some € traveller cheques and took ATM withdrawals as well and to be honest it was quite comparable.
Can't speak for Hong Kong or Malaysia sorry