The four major banks in China are Bank of China, ICBC, China Construction and Agricultural Bank of China. They all have branches and ATMs throughout China. I have a Schwab debit (no international fee) and Chase debit card. Only once have I had a problem using my ATM card in Guilin, Schwab was rejected by machine so used my Chase card which was accepted (Chase promptly charged me a pretty penny). Otherwise I used the Schwab card in Beijing and Shanghai plenty of times with no issues.

Otherwise I highly recommend using an ATM to get RMB. You might not need any RMB though until Guangdong as you can use your credit card for food in PEK airport. But if you want some pocket cash, just find an ATM.