The Slovakian currency is the crown which they call the koruna. I went last November and they do accept euros quite happily and most items are priced in SKK (crowns) or euros.
Might be sfer to use your credit card rather than debit card as the latter is giving direct access to your current account - a problem if any theft or fraud occurs. If you contact barclaycard and tell them where you are going they will tell you what it costs to withdraw local cash.