nobody?

I took an airport transfer from my hotel for around 25 euros, as I arrived at about 1 am in Kiev. On the way back, I took a shuttle from the main railway station, which was cheap although I don't remember how much. I think it took about half an hour in the middle of the night in a car, longer on the shuttle. You can find proper information on this sort of thing by googling.

Here's my trip report from last August http://www.fodors.com/community/europe/ukraine-trip-august-2011-kiev-lviv-chernivtsi-odessa.cfm

I can't think of too much I would do in such a short time (are you departing Kiev city at the time stated, or is that your flight time?), but I do tend to get quite nervous about setting out to the airport early. I suppose wander around and have dinner somewhere on the evening then the next day something like walk down Kreschatyk and see Independence Square (Maidan Nezalezhnosti), up the hill past St Michael's monastery (not really worth going inside, it's all newly constructed) and then turn left to go inside St. Sophia's if you have time. Or stroll down Andreyivski Uzviz to see the beautiful Rastrelli church and people selling antiques or "antiques".

I really enjoyed going up the Rodina Mat statue at the War Museum, to a height of 91 metres (and you get to pop out the top of the shield) but whether you'd have time I don't know. I had to wait around while a group of people was assembled for the ascent, and the guide spoke only Russian (I understand a bit of Russian, but luckily someone else translated as well). Personally I would be a bit nervous doing that with the time constraints, but perhaps you're braver than I.