Been there quite a few times altho not so much recently. Actually really liked it. Altho I haven't been to Nigeria and have a relatively high tolerance of developing countries, I'd probably much rather go with Ukraine than Nigeria.
Some good food. Don't bother getting the Chicken Kyiv - it's no better than anything else. If you're on your own (in particular), Puzata Khata is a good place to get Ukrainian food because it's mostly a buffet type deal (at least it was when I was there) - try the syrniki: http://www.puzatahata.com.ua/eng
Baraban was a funky little hangout too: http://www.lonelyplanet.com/ukraine/kyiv/restaurants/bar/baraban
A fair amount of people speak English if you ask around but it's not an English-speaking place, IYSWIM.
"I imagine it to look like "movie" soviet state"
Not really - it's pretty modern and colourful in Kyiv. Never been to Poltava but we're just over 20 years since the collapse of the Soviet Union, so it's not going to be like Pyongyang. (Not saying it'll necessarily be pretty either).
Good luck. Be sure to form a personal relationship with the other side before diving into the "work" - Ukrainians are not a clinical/formal people, generally speaking (although who is?). Apologies if this is patronising - you seem to be fairly well-travelled.