3. Online at VK.com
Top Foreign Press, run by a guy named Andrey, has over 200 titles; he gets them from the UK, Japan, the US, Germany, France, and Italy. The magazines come in weekly on varying schedules. He has some back issues and also takes special orders.You can check out his online catalogue here and it is available in English. There is currently a temporary delivery gap for English language news weeklies such as Time, The Economist, and Newsweek, but the German language ones are available. He also has magazines for teenagers. The downside is that prices are about double the suggested retail price.
The American Center near Kitay Gorod/Taganskaya has a 10,500 book library (some are available for circulation) and 82 periodicals that you can browse but can’t take out of the library. You can search for books in their online catalogue too. Anyone can come but you need a passport to get into the building.
Update May 2015: There is now a group on Vkontakte that has PDFs of English magazines and some e-books. Check them out here.