There are a large number of UNESCO heritage sites on the territory of modern Russia.

Here is their list:

The historic center of St. Petersburg and related groups of monuments
Kizhi churchyard
The Kremlin and Red Square, Moscow.
Cultural and Historical Ensemble of the Solovetsky Islands
Historical monuments of Novgorod and its environs
White monuments of Vladimir and Suzdal
The architectural ensemble of the Trinity Lavra of St. Sergius in Sergiev Posad.
Church of the Ascension, Kolomenskoye.
Virgin forests of Komi
Lake Baikal
Volcanoes of Kamchatka 22
Golden Mountains of Altai
Western Caucasus
Curonian Spit *
Ensemble of the Ferapontov Monastery.
Historical and architectural complex of the Kazan Kremlin.
Central Sikhote-Alin
The Citadel, ancient city and fortifications of Derbent
Ubsunur Basin *
The ensemble of the Novodevichy Convent.
The natural system of the Wrangel Island Nature Reserve
The historical center of Yaroslavl
Struve geodetic arc *
Putorana Plateau
Lena Pillars Nature Park
Bulgarian Historical and Archaeological Complex
Assumption Cathedral and Monastery of the Island City of Sviyazhsk
Landscapes of Dauria *
Churches of the Pskov School of Architecture
Petroglyphs of Lake Onega and the White Sea.
Astronomical observatories of Kazan Federal University