These are all great suggestions, thank you.
I have previously been to Chernovtsy:
http://www.josephroling.com/photos/ukraine/ukrainetrip.html
However tickets, round trip on KLM and MDK were only $800 and now they're $1200-$1700.
With its close proximity to Hungary, Poland or Moldova, I thought perhaps a lower-priced option existed and I have zero experience with Ukrainian trains. Unless I'm missing something, Ukrainian trains tend not to post their rates online, so it's difficult to assess the total cost.
I will start exploring some of the suggestions posted. Travel and optimism are interwoven for me, so I am hopeful a satisfactory solution exists :)
This is a great site and the community has been very friendly.