Here is a representative sample of nine Russian cities with their Anglicized and Russian Cyrillic names:

The Hermitage Museum in St. PetersburgMoscow (Москва) — Russia's gargantuan capital is one of the world's greatest cities and has endless attractions to offer an adventurous visitor
Irkutsk (Иркутск) — the world's favorite Siberian city, located within an hour of Lake Baikal on the Trans-Siberian Railway
Kazan (Казань) — the world's capital of Tatar culture is an attractive city in the heart of the Volga Region with an impressive kremlin
Nizhny Novgorod (Нижний Новгород) — often overlooked despite being one of the largest cities in Russia, Nizhny Novgorod is well worth a visit for its kremlin, Sakharov museum, and nearby Makaryev Monastery
Saint Petersburg (Санкт-Петербург) — Russia's cultural and former political capital is home to the Hermitage, one of the world's best museums, while the city center is a living open air museum in its own right, making this city one of the world's top travel destinations
Sochi (Сочи) — Russia's favorite Black Sea beach resort has been largely unknown to foreigners, but that is set to change in a major way when it hosts the 2014 Winter Olympic Games
Vladivostok (Владивосток) — often referred to (somewhat ironically) as "Russia's San Francisco," full of hilly streets and battleships, this is Russia's principal Pacific city and the terminus of the Trans-Siberian Railway
Volgograd (Волгоград) — formerly Stalingrad, the scene of perhaps the deciding battle of World War II, and now home to a massive war memorial
Yekaterinburg (Екатеринбург) — the center of the Urals region and one of Russia's principal cultural centers is a good stop on the Trans-Siberian Railway and an arrival point for visitors to the Urals, the second russian financial center.
Other destinations

Lake Baikal, the deepest lake in the worldKizhi — one of the most precious sites in all Russia, Kizhi Island on Lake Onega is famous for its spectacular ensemble of traditional wooden churches
Lake Baikal — the "pearl of Siberia" is the world's deepest and biggest lake by volume and a remarkable destination for all who love the outdoors
Trans-Siberian Railway — perhaps the longest train route in the world, this itinerary takes you across the entire Asian continent (and a good chunk of Europe) the long way
Mamayev Kurgan — overlooking the city of Volgograd, this is the memorial on site of the the twentieth century's most important battle, Stalingrad