New Arbat Street: Located near Old Arbat Street, this street offers a contrast from the touristy pedestrian-only thoroughfare. New Arbat is perhaps where Moscow's rich are the most visible, as some of Moscow's most expensive restaurants and nightclubs are located here. There are some reasonably priced cafes, however. The street is lavishly lit up at night and is always very lively. Also, check out Dom Knigi (House of Books) on New Arbat. It's not as impressive as the St. Petersburg store, but probably the best bet for books in Moscow. Metro: Arbatskaya (Light Blue).
Tverskaya Street: This street starts from the Kremlin itself and runs northwest in the direction of Tver (hence the name) and Saint Petersburg. For that reason the road was a very important thoroughfare in Tsarist Russia. It is now Moscow's most fashionable street, with several prestigious boutiques. It is also lined with cafes, restaurants, coffeehouses, a couple of theaters, and several hotels, including two locations of the Marriott. Most of the street's architecture doesn't actually have much history to it, though along the way you will find Russia's first, and the world's busiest, McDonalds. The statue of Pushkin at Pushkinskaya Square is a very popular meeting point. Walk its length. From Red Square to Belorusski Train Station is about one hour and is a great way to see the most famous street in Moscow. Take a peek inside the Yeliseev Grocery Store, Moscow's answer to Harrod's food halls, to see the restored ornate interior. Metro: Tetralnaya, Tverskaya/Pushkinskaya, Mayakovskaya, Belorusskaya (depending on what part you want to exit at).
Gorky Park: Easily the most well known of Moscow's many parks, Gorky Park is packed with a number of theme park rides, cafes, places to stroll, and a quaint-looking pond, all straddled alongside the Moskva river. Gorky Park is a very popular place for Muscovites of all ages. In winter it's a popular place to ice skate and it hosts an ice sculpture competition. Metro: Oktyabrskaya, Park Kultury (it's a walk along the Sadovoye Ring Road from either of them - an easier, downhill stroll from the former, or a more scenic route, over the Krymsky Bridge, from the latter).
Garden of Fallen Monuments: Where many infamous statues in Moscow were placed after the Soviet collapse. See Dzherzinsky, Stalin, Brezhnev, and others. Adjacent to the New Tretyakov Museum, which houses 20th century art. After the Pushkin Museum and the Tretyakov Gallery, this is worth seeing. Metro: Oktyabrskaya.
Russian State Library: One of the largest libraries in the world. Anyone (Russian or foreign) over 18 can view electronic media for free, other items may be viewed by purchasing a "Reader's Card" (a photo id to gain access to physical materials). Previously received a copy of every book, musical score, & map published in the USSR, it now only receives a copy of every Russian book. The military reading room receives over 15,000 readers a year.
State Museum-Reserve Tsaritsyno: A beautiful reserve in the southern part of Moscow, its nucleus being the largest palatial ensemble in Russia. Constructed between 1775 and 1796 to be the residence of Catherine the Great, the ensemble was abondoned after her death and turned into ruins during following centuries. A decision had been reached in 1984 to completely restore Tsaritsyno architectural and park ensemble. Majority of the architectural monuments have already undergone restoration, Grand Palace having completed by 2007. Exhibitions and expositions of the museum demonstrate various pages of Tsaritsyno history and rich collections of arts and crafts. Metro: Tsaritsyno, Orekhovo.