I agree about the BYKI software. It combines visual and audio material and uses a method that, at least for me, seems pretty effective.
Also, have you considered the Pimsleur Basic Ukrainian course?
It's only $22 from http://www.pimsleuraudio.com
The Basic version really is very basic, but it's an excellent way to start because the method helps you 1) pronounce words and phrases correctly and 2) really remember those words and phrases. If you don't know a word of Ukrainian and especially if you don't know any other Slavic languages, you might want to try it. That course alone probably wouldn't be enough to get by in every tourist-type situation, though.
I just checked and apparently the Teach Yourself series has Ukrainian (by Olena Bekh and James Dingley). That's also a very good series and will definitely give you enough to get by comfortably. It comes with a book and cassettes (or audiobook). Amazon has it.
Also, you might try something like http://www.livemocha.com to find a native-speaking conversation partner, too.