When do you arrive?
They close the main street in the center of town, Khreshatik, daytime on the weekends so it's a nice place for a stroll.
There's a great nightclub right next to the stadium if you're there on Saturday night. It's called D-Lux. Off-the-hook. Don't expect much music-wise but the eye candy is stunning. If you walk toward the stadium from the end of Khreshatik you walk up the left side of the territory along Petrivska alley.
Not far from there, there's a very fashionable bar in the park where the statue of Volodymyr the Great is.
If you walk straight up hill from Independence Square (Maidan Nezalezhnosti) on Sofievskaya vulitsa for about 10 mins. you can see the Sofia cathedral which is nice. Good Italian restaurant nearby there called Da Vinci Fish Club.
The Mother of the Motherland statue overlooking the river is a cool thing to see as well, as is the big cathedral and monastery nearby.