Ukraine is the largest country in Europe (if Russia is excluded) but is still not part of Schengen. It was part of Soviet Union before becoming independent in 1991. Bordering Black sea on one side and Carpathian mountains on the other, it takes a little over an hour by flight to travel from capital Kiev to Lviv on the western side and Odessa on the eastern side. Most travellers to Ukraine are from Europe. I spent about a week in Kiev with a full day trip to Chernobyl, the site of the catastrophic nuclear accident in 1986.
Kiev, Lviv and Odessa are the 3 popular destinations in Ukraine. But avoid areas closer to Russia border.
Kiev or Kyiv, the capital of Ukraine has a number of churches and parks. The city centre is fairly impressive.
Chernobyl, the site of the worst nuclear accident, is worth a visit.
