There are two Credit Card issuers I know of (from the top of my head) that do not charge any fees on currency transactions:
- Halifax Clarity ("free" in the EU; there may be a percentage elsewhere)
- Post Office ("free" everywhere).
There are probably a few others.
They use something very close to the wholesale (city/mid) rate to work the transaction. You DO NOT pay interest on purchases if it's fully repaid by the due date and I recommend a Direct Debit to do exactly this.
You DO pay interest on cash withdrawals but that can be largely avoided - see below. With these two cards, there are no fees other than this - unless the ATM itself levies one.
You can apply for cards issued by third parties such as these; you are not "tied" to your own bank. I strongly suggest that you apply for at least two. So doing gives you some contingency in case of (say) loss of a card, etc. And take your existing card as well, even if it has fees, as a further backup. Keep it safe (eg in your hotel) unless needed.
Fee-free cards used in this manner can save 3-5% over anything you might get from an exchange bureau (ignoring unpredictable market fluctuations) because of their use of that whoelsale/middle rate as the basis for the exchange. And, yes - ALWAYS pay in local currency.
How to largely avoid interest on an ATM withdrawal:
Take with you a means to get online access to your bank and to your Card account. Make your withdrawal. Check daily and WAIT until the withdrawal is posted to your account. That day - pay it off in full, manually. You may end up with only one or two days' interest (pennies). In theory, you only need pay an amount to cover the withdrawal itself and that should be applied with priority over other spending, but I did once encounter a legitimate "loophole" to do with a carried forward balance so for confidence, I'd pay the entire balance off.
And of course you minimise your use of cash by using the card instead, even for small amounts, unless the merchant won't let you.
Finally, if they issue your card with a relatively small spending limit, there is nothing to stop you making ad-hoc payments regularly, so as to bring you back well below your limit.