Art galleries can be viewed in all major cities of Russia. Moscow and Saint Petersburg each have two art galleries that can be called world-class museums, but other cities also offer interesting paintings by Russian artists.
In Moscow, you should definitely visit the Tretyakov gallery, where you can see paintings by Russian artists, as well as the Pushkin Museum, where there is a very interesting collection of paintings by impressionist artists.
In St. Petersburg, all tourists go to the Hermitage, where you can see paintings by all the major artists in Europe. Russian Museum is a great place to visit if you are interested in Russian art.
Other cities have collections of famous Russian artists, mostly from the 19th century: Aivazovsky, Perov, Shishkin, Repin, Levitan, Polenov, Bryullov, and many others.