Can a Ukrainian girl or Moldovan come to see you anywhere instead of you going to her country to see her? What kind of visa do they need to get? I know russians can go to Prague for example.
Cheapest place to visit would be Istanbul. She could get a visa at the airport for $10, and if you're American, $100 for you. But accomodation would be a lot cheaper than in Prague. However, most girls are terrified of meeting in a third country.