First of all, the St. Sophia Cathedral is a piece of history to behold. This church dates far back to the 11th century. It boasts a dome adorned in green and gold; it was a hub for Soviet Russia. Although it has seen damage over the ages, it has been kept up and is in beautiful repair to this day. Its design style is now a combination of over nine centuries of architecture! It boasts a unique variety of centuries-old frescoes and mosaics.
Another great locale is the Kiev-Pechersk Layra (Caves Monastery) which dates all the way back to the 11th century. This cave was homebase to the monk Anthony. After Anthony settled here, scores of people followed and lived in the caves. To this day, the area is active and reflects the history of its Orthodox Christian roots.
Third, the Great Patriotic War Museum is a must to go to on your Ukraine visit. One of the most magnificent sites is near the museum: the statue of the Motherland (it looks similar to the statue of liberty, only holding a sword). Outside the museum, war tanks that are no longer used can be seen with flowers painted on them, plus to a statue dedicated "to the Fallen" which is a memorial for the many who died in the war.
You cannot miss the local town in Western Ukraine called Kamyanets-Podilsky. It retains its medieval feel and is actually set on a giant rock bed. This fact alone makes the town a site to see!
Finally, you should go south to Yalta, which is referred to as the "Pearl of the Crimea." Near this You'll find the Livadia Palace. Its historical importance is high, as it's where the map of Europe was changed in 1945 in a meeting between Roosevelt, Churchill and Stalin.