Well, don't miss a chance to go back to Ukraine to visit Crimea eventually. Trust me - it's worth it.
And have a good time staying in and around Kharkiv.
BTW, here are some hints for the city guests if you like - http://football.kharkov.ua/2012/5/8/euro-2012-kharkiv-crash-course-part-1-arrival


Actually, there are lots of things to do in Kharkiv =)
The city has been a capital of Ukraine during USSR and it has been economic, political, historical, industrial and education center and nowadays it is one of the largest cities. And such cities always have plenty of things to do =) Check this book Travel Ukraine: Kyiv, Kharkiv, Lviv, Donetsk. - you will find a lot of useful information what to do in Kharkiv, what to see, where to eat. You will find a lot about prices, useful tips and links. To my opinion this guide is one of the best written so far about Ukraine..