The national tourism website can give you food suggestions:
http://www.traveltoukraine.org/cuisine.htm
(Most of what's there looks remarkably similar to Polish cuisine. Based upon that, I can recommend trying the Holubtsi which seems to be the same as Gołąbki in Poland)
Same as golubtsi in Russia. Cabbage leaves stuffed with mince. When I was there if they appeared on the menu, which they did at least every other day if not more frequently, they were there for the duration breakfast, lunch and dinner. I'd be a rich man if I had a rouble for every golubyets I have eaten.
I'd put St Sophia and St Michael at the top of my list. Maybe stroll along Khreshchatyk past Independence Square, then go left somewhere and down St Andrews Hill to the riverside suburb at the bottom - forget its name. I wouldn't really bother with the Motherland statue unless you're a Texan who thinks bigger is better.