I recall a trip I took to kharkov from Sumy. We traveled by taxi to the outskirts of the city then took the Metro from there. The city is older and looks like an older soviet style city. Not many modern buildings like Kiev but like most city's in Ukraine there is some interesting sites and things to do. Kharkov was the former capital when the country was part of Russia tho not as old as Kiev it is big. They have an indoor water park that offers theme nites and fun for the whole family. The zoo is quite small but worth a look if the weather is good.
I spent about an hour looking and feeding the animals taking a few pictures along the way. You can feed some of the deer and other animals with food purchased from vendors.
I also visited a church and a monastery that was quite old. A word of caution to enter the monastery you must wear pants, no shorts allowed. I was able to get a few pictures from the entrance.