[TimSchumann]

Sounds like you're getting a pretty raw deal. I wonder how common problems like this are. Anyway, here's some thoughts on the matter.

You probably thought of these:

  Find a new bank in Ukraine that will allow you to hold USD denominated deposits.
  Find a bank in the US that will allow a nonresident to open an account.
  Find a bank in another country with USD denominated deposits.

I'm not sure if the inverse problem is true, but I know that as an american creating a bank account in another country can be a headache. Mostly due to compliance issues with US federal regulations. Maybe that's the case all around, I'm not sure. There is no real incentive for any country to do anything but force their particular brand of kool-aid on you so I'm guessing it's going to be hard to find anywhere outside the US that allows someone of average means (read not really rich) to keep funds on deposit that aren't denominated in local scrip.

Might not have thought of these:

  Bitcoin (Yes, Seriously)
  Trusted Friend or colleague 
  Other Financial Instruments like stocks, bonds, money market accounts

Also, just a reminder to do your own due diligence on the legal aspects of all of this wherever you're operating.