As others have noted, you are almost always better off paying in local currency as the credit card company's exchange rate will be at least as good as the hotels.
The only possible exception is if your booking specified the price in dollars. In this (rather rare) scenario, in order to pay in local currency, the hotel will convert your price into local currency at some exchange rate, possibly an unfavorable one and then the CC company converts it back into dollars (or your home currency).
I've had something similar happen once (in Prague) where the price was quoted in EUR but they could only accept local currency for CC payments. They did however use a fair exchange rate. I could also have just payed in EUR if I had had cash which I didn't. If they had accepted EUR payments via CC that would have been better given the circumstances.