Don't go to a bank, go to a currency exchange.
This one is conveniently located on Rafael Melgar and has decent rates. But the first time you go, you have to wait for them to fill out some sort of official paperwork. Keep the form they give you and subsequent exchanges will be fast.
Banregio Exchange · San Miguel de Cozumel, Quintana Roo
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Or go to one of several "Money Exchange San Jorge Sucursal" along Ave Pedro Joaquin Coldwell. The rate will be very close to Banregio and there is no paperwork. You will need to bring your passport (this is true for all money exchanges in Mexico).
They all post the rate outside so you will know what you are getting and they'll show you on a calculator before doing the actual exchange. None of these places charge any fees beyond what is built into the rate which is normally around 3% below inter-bank rates. This is much better than you'll get from local businesses.
