If you pay by Dollar (or home currency)
The hotel will add a charge for this, hence you will be paying more.
If you pay by local currency the exchange rate will be decided by the credit card company or bank.
These exchange rates are much better than the hotel rates.
Check this Visa page for more information regarding this service for Visa holders.
AFAIK, Other companies have similar services so this applies to all other credit cards.
travel.stackexchange.com/users/10051/Nean Der Thal
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.
travel.stackexchange.com/users/1488/Kris
The big advantage of paying in your own currency is that you know the exact amount in your currency you were charged, and you can do your expense report right away.
You don't have to wait for your statement or do any currency conversions on the expense report.
Since you're not spending your own money in this case, it seems attractive.
I believe it's offered as a "service" and a "convenience" for business travellers.
Like many things hotels offer to business travellers, it's a good revenue source for the hotel.
Think about car rental places that will fill the tank for you as a convenient service :-)
I doubt very much you would save money paying in your own currency.
If the early or easier access to the number isn't worth anything to you, don't take this option.
If you are familiar with the exchange rate, you could ask them what rate they'll use to decide whether to take it or not, but I would be very surprised to hear that it ever saved anyone any money
: that's not why they offer it.
travel.stackexchange.com/users/46/Kate Gregory
If the country you are traveling through faces major inflation of its currency, it might be worth paying in local currency (if they allow you to).
At the end of the eighties I was in a south American country with huge inflation rates where once people got their salaries they rushed to the shop to spend it all.
The same amount could just drop in value by tens of percentage points within a day.
I am not so sure if these hyperinflation rates still occur, but it is worth considering when deciding between paying in the local currency or your home currency.
Personally I apply the "when in Rome do as the Romans"-dogma.
Meaning that I choose to pay in the local currency.
There is no logic behind this choice, other then to keep things simple.
I don't want to account in two currencies, at least until my final accounting where I sum up what a trip cost me in total.
travel.stackexchange.com/users/None/
If you pay in local currency, you control the exchange rate, or at least international banking rules do.
If you pay in dollars, the shop owner applies whatever exchange rate is best for him.
This is usually not in your favor.
If you know the official exchange rate at the time of your transaction and are able to make quick comparisons in both currencies, you can ask both prices and choose the best one for you.
travel.stackexchange.com/users/241/mouviciel
Recently I had to pay for a hotel in a foreign country using credit card, and the guy at the hotel asked me if I wanted the bill to be paid in the local currency or in US dollars. I didn't even know I had this option.  Which currency should I have chosen if I wanted to pay less? What are the pros and cons of paying in each currency?
Paying by credit card while overseas cheaper in US dollars or in the local currency?
travel.stackexchange.com
<budget><money><international-travel><payment-cards>
travel.stackexchange.com/questions/9012
travel.stackexchange.com/users/2721/hooray
You can calculate the best option if you see both prices, but it is almost always cheaper to pay in local currency as the credit card company's exchange rate will be at least as good as the hotel's. On the other hand, paying in dollars means that you know the exact amount in your currency for your expense report. Paying in local currency is considered the better option, unless you need the value in dollars to make a travel expenses claim. The exchange rate is different depending on the currency you pay in and it is more favorable when you pay in local currency. If you know the exchange rate, do quick calculation and decide at the time of making the purchase.
Paying in local currency is better than paying in dollars as the exchange rate is controlled by the banking system. If the country you are in has inflation this may make it a better option too. Paying in dollars is better when you need to know the dollar value for travel expenses. However the shopowner decides on the exchange rate. If you know the exchange rate, do a quick calculation and decide which is best.