The flat rate taxis from airports (they are present at several) do cost more than the metered taxis, but the advantage is that you can pre-pay (including by credit card, I believe), and you know the price without worrying about the efficiency of the meter, whether you'll pay more due to traffic, etc. But you do pay extra. Exchange rates at airports are generally not great anywhere. Nothing unique to GRU. If you can get money from your credit card or debit card, the rate should be the same at the airport as elsewhere. I use a Citibank debit card at Banco do Brasil at the Fortaleza airport. Note that Sao Paulo's traffic can be horrendous, and the airport, in Guarulhos, is a ways away. There are some quite nice hotels in Guarulhos, but if you're not just staying at the Hyatt as a place to rest, going to SP could make sense.

Of course, you could always ask the Hyatt about the best way to get to their location.