Visit the war museum to have a seat in some old Soviet WWII weaponry in a proper hands-on fashion. Find out about the defense of Ukrainian Russia.
If you get time it's worth visiting the island parks on the Dnieper. Walk up the main boulevard for 5 blocks from European Square and then turn left. Continue down to Shevchenko park where you'll find a bridge that takes you across to one of the island parks. Here you can enjoy some relatively clean air, take a quiet stroll in the center of the city, pick up an ice cream or beer, and take a ride on some of the features of the old Soviet-style funfair.