When you travel to Ukraine you should make a list of places and cities you want to visit according to your interests. But Lviv is a must see city because you won't see authentic Ukraine if you don't go to this wonderful city.
Lviv is a western Ukrainian city situated just 70km from Polish border. The population of the city is 730,000 people, main nationalities are: Ukrainians — more than 70%, Russians— nearly 10%, Poles — 1%, Belarusians, Jews and other. The vast majority of people speak Ukrainian language. But the situation wasn't always like that, imagine that less than 100 years ago 60% of people were Polish and Polish was the main language. The thing is that Lviv was a Polish city until the Second World War; it explains the abundance of old sophisticated architecture.
Being the main cultural centre of Ukraine, "the city of lions" can offer a great variety of attractions. You can just walk around the city and get a great pleasure by observing the great architecture in the center of the city which is included into UNESCO World Heritage List. Among popular tourist places are Lviv National Opera house where theatergoers can watch classic and modern performances, Lviv National Art Gallery, the Lviv National Museum, the National Museum, statue of Leopold von Sacher-Masoch, etc. A great religious diversity of the city can explain the variety of churches and cathedrals. There also was a big Jewish community, nearly 45 synagogues were built in a city but closed under the Soviet power. A separate topic is different conceptual cafes and restaurants as for example "Kryivka" designed as a secret shelter of Ukrainian partisans or Jewish café where you won't find prices in the menu, you will have an opportunity to bargain on price with a waiter.
Many eminent and famous people lived in Lviv: Sholem Aleichem, Yuri Bashmet, Ivan Franko, Leopold von Sacher-Masoch, Svyatoslav Vakarchuk and a lot of other important personalities.
I am pretty much sure that Lviv will be one of the cities which you won't be able to forget after you've travelled to Ukraine. These cobblestone roads, paved narrow streets, majestic architecture and special warm atmosphere of antiquity can't leave somebody untouched.