The only way to get a free ATM is to have a Thai bank Account.
Unfortunately they all charge the 220 baht fee for any international transaction.
Also be aware, every ATM will ask you if you want to use their special "Conversion factor". Always answer NO, "Continue without conversion" as the rates your bank use will be much better (At least from the USA they are).
The other way is if you have a smaller bank in the USA that refunds the ATM fees, but I'm not sure they refund the international fees (only ATM fees from the other US banks).
Also, if you need a superrich and rode the Airport Rail Link, there is a branch at the PhayaThai - Airport Rail Link station now.