The Historical Complex of the Sheptytsky National Museum is a serious stop for travellers interested in Ukrainian religious art and cultural history. Its collections connect icons, church art, and the figure of Metropolitan Andrey Sheptytsky, one of the central patrons of Ukrainian culture in Lviv.
It is quieter and more specialised than the city's headline churches and squares, but that is the point. Visit when you want to understand Lviv as a Ukrainian and Greek Catholic cultural centre, not only as a handsome Central European old town.