Kremenets is a nice little town in Ternopil Oblast that is worth the stop. Some say the fortress here was established in the 8th century but the earliest mention of it is 1064. It changed hands many times over the years, including 7 times between 1917-1920.
You will find a castle here that is in ruins but still rather interesting. In the city center there is a huge cathedral to walk around. You can easily spend a day here seeing things.