You can get a decent introduction to the capital in just a few days, leaving time to travel to St. Petersburg.
Start with a stroll across Red Square, a tour of St. Basil's Cathedral, the shopping arcades of GUM, and, if you're a devoted student of Soviet history and/or embalming techniques, the Lenin Mausoleum. Then walk through Alexander Garden to reach the tourist entrance to the Kremlin. Plan on spending the better part of your first day exploring the churches, monuments, and exhibits within the grounds of this most famous of Russian fortresses. On the second day, spend the morning sightseeing and shopping on ulitsa Tverskaya. In the afternoon, head to Kitai Gorod; this neighborhood has churches and historic buildings on ulitsa Varvarka, which extends from the eastern edge of Red Square, just behind St. Basil's. Try also, toward the end of the day, to squeeze in a stroll across ploshchad Teatralnaya to see the Bolshoi and Maly theaters. If there's time, don't miss the Gulag Museum. Devote the third morning to the Tretyakov Gallery, which has the finest collection of Russian art in the country. In the afternoon stroll down the Arbat, where you can find plenty of options for haggling over Russian souvenirs.
On the fourth day explore ulitsa Bolshaya Nikitskaya and the surrounding neighborhood, with its enchanting mansions, and the chic and attractive neighborhood around Patriarch's Ponds. Devote the fifth day to the Pushkin Museum of Fine Arts, the Cathedral of Christ Our Savior, and an exploration of some of the streets in the surrounding Kropotkinsky District. Come back the next day and walk from the Russian State Library to the Kropotkinsky District. Be sure to include the Pushkin Memorial Museum and a walk along the naberezhnaya Kremlyovskaya (the embankment of the Moskva River) in the late afternoon for the spectacular views of the cupolas and towers of the Kremlin. Depending on whether your interests tend toward the religious or the secular, you could spend your last day visiting either the New Maiden's Convent and the adjoining cemetery or Gorky Park and the Tolstoy House Estate Museum, where the legendary author of Russian classics once lived.