Card limits to the rescue (if you have an internet connection)
Our strategy is to set a limit on the card so that we can at most withdraw the amount we intend to withdraw. We typically use Revolut whilst abroad, so I will just put all the money I don't intend to withdraw into a 'pocket' or 'vault' or whatever they call it now (imagine a savings account without interest, the point is that you can't access it by paying with your card). Typically this means that I will have exactly 200 euros available at the start (as that's the monthly free withdrawal limit ).
Then I go to the ATM, and try to withdraw exactly 200 euros. If a fee is mentioned - and I deem the fee acceptable - I will adjust the amount I try to withdraw downwards. If a maximum withdrawal is mentioned, I adjust the amount available on the card before actually trying the withdrawal.
The point is that if there is an unadvertised fee (something I have seen only a handful of times in the last 3 years (25 countries or so)) this will cause the withdrawal to fail, and it will show me the fee by looking at the failed withdrawal notification.
Once with an ATM that felt shady (it was a tourist focused ATM, and it didn't ask whether we wanted to convert or not) we even just tried to withdraw whilst we intentionally had 0 euros on our card, to check whether it wouldn't do something weird (it did, so we ended up not using it).
Online research
In general the online communities of 'travel banks' (like the Revolut forums) are amazing places to find advice for ATMs that don't charge withdrawal fees (to be fair, these lists are often outdated and/or not completely accurate (e.g. in some countries visa cards might be charged whilst mastercards might not be on the same ATM), but they are amazing starting points). I will typically try to find a dedicated thread about a country I am travelling to, but here is for example one attempt to collect everything into a single spreadsheet: https://community.revolut.com/t/the-ultimate-free-atm-list-travelling-by-country/61491 (For example in that same thread someone mentions that in Rwanda I&M bank doesn't charge for a VISA card in 2019). Of course, this is more likely to be accurate if you use Revolut as well, but as a starting to point to figure out which ATMs to check out it's absolutely perfect no matter what.