Nobody ever mentions Belarus for banking; definitely not a compliant country. Ignoring the present political situation, it's arguably more stable, safe, and developed than Ukraine, and better than Russia in some ways. Of course there's the Putin/Union factor to consider, but for some that might be a bonus (how much money and goods flows between these two countries! BY is a gateway economic zone for skirting Russian or Iranian embargoes). It's possible to open both personal and business accounts in BY, including remotely via PoA. Use case might vary, but there's some big banks there including RBI and Bank of Georgia. Idea (PL) has a presence there too, but since they sold RU and UA branches, BY might be next, so I wouldn't consider them. Belarus has some nice cities and nature, well developed IT economy, and it could be used to park some spare change out of arms reach fairly easily.
Ukraine might be worth considering using one of the foreign held banks (including RBI, as in BY), but I'm always skeptical about EDI between foreign branches. What's stopping Deutsche Bank Ukraine from phoning home to Berlin to report on your Kiev holdings? Also, when 2008 happened, hilarity ensued. Gov't offices were closed and business and banking basically froze. Maidan wasn't much better, so all we need is another Crimea to happen in Donbass, and anybody can guess what's next. haha. But I would feel reasonably safe in a foreign bank over there. Personally, I've used Citibank in Ukraine doing transactions between USA. It was smooth and easy, the fund transfers were instant. I haven't done this for over a year, so who knows what it's like now.
(Side note: if you want some laughs, look on YouTube for "ukraine duma fight" or similar. Comedy gold, every parliament should be like this. Shoes, umbrellas, and fists flying. Klitschko should have faced off more often in the centre ring, he would really have brought the fight to corruption.)