Traveling to turkey the hotel is in euro. Which is a better rate pay with actually euro or place on my US credit card? I can exchange before I leave home but not sure if I want to carry that much on me.
The fewer times you exchange the same money the better. If you don't get euros from a cash machine in Europe, then you pay a pretty poor exchange rate to get them from your bank at home. I would pay the hotel with my credit card and want it to be charged in Turkish Lira. Although they have advertised the price in euro, the hotel will probably convert that value to Turkish Lira at the daily rate they have posted. Again, not as good as the rate banks pay each other, but you can't get that rate.
You need to check your credit card's policy on extra fees. Some charge a foreign transaction fee of up to 3%. But the actual exchange rate will be the interbank rate at that time. And even at 3%, that is cheaper than any currency exchange process will be and usually no more than your ATM fees.
Getting cash from an ATM is always cheaper than exchanging currency. And some places might offer a cash discount. Again, check your bank's policies on fees.
One thing to watch out for. Sometimes merchants and even ATM machines will ask you if you want to convert your transaction into your own currency. Sounds so nice and helpful... It's NOT. It's a way for the merchant and their bank to set the exchange rate, which is higher and they get a cut. Your bank is perfectly capable of converting on their own.
My experience was that while hotels posted prices in Euro, they actually got payment in Turkish Lira (either cash or credit card). I chose to pay with cash from ATM's (found as prevalently in Turkey as anywhere else).