Russian analytical agency TurStat published a list of five most popular tourist sights in Russia in 2018 and all of them are on the UNESCO World Heritage List:
1. Red Square, Moscow: 20 million visitors a year

Although most famous for its political symbolism, Moscow’s Red Square (Krasnaya Ploshchad) was actually named for its beauty: the word “krasnaya” which means “red” in modern Russian language actually meant “beautiful” in old Russian language. It is located in front of the eastern wall of the Kremlin (nowadays the official residence of the president of Russia) and bounded by three beautiful buildings: the State Historical Museum, the GUM department store, and St. Basil’s Cathedral. It was declared a World Heritage Site in 1990.
2. Peterhof, St. Petersburg: 5 million visitors a year

The Peterhof Palace is a series of palaces and gardens located in Peterhof, just outside St. Petersburg. Majestic and covered in gold, it is often referred to as “The Russian Versailles”. Palace of Versailles by Louis XIV of France actually was the inspiration for Peter the Great who had the desire to build an imperial palace in the suburbs of his new city – St. Petersburg. It was declared a World Heritage Site in 1990.
3. Kremlin, Kazan: 3 million visitors a year

The Kazan Kremlin is the main historic citadel of the Republic of Tatarstan, situated in the city of Kazan. It is the only surviving Tatar fortress in Russia and an important place of pilgrimage. It was declared a World Heritage Site in 2000.
4. Trinity Sergius Lavra, Sergiev Posad, Moscow region: more than 2 million visitors a year

The Trinity Lavra of St. Sergius is the most important Russian monastery and the spiritual center of the Russian Orthodox Church. It is situated in the town of Sergiyev Posad, about 70 km to the NE from Moscow. It was declared a World Heritage Site in 1993.
5. Baikal, Irkutsk Region and the Republic of Buryatia: more than 2 million visitors a year.

Lake Baikal is considered to be the oldest existing freshwater lake on Earth as well as the deepest continental body of water. It is situated in the mountainous Russian region of Siberia, north of the Mongolian border and circled by a network of hiking paths called the Great Balkan Trail. It was declared a World Heritage Site in 1996.