I agree with all that was said about the visa thing. One of the advantages of being the Russian citizen is that you don’t need to deal with our diplomatic bureaucracy when travelling in & out the country. :)

Concerning the place to stay I also agree with the suggestion to stay at someone’s place to experience Russian hospitality (otherwise your trip here would not be accomplished). But if you better prefer to stay at less informal place here are some sites about the hotels:
http://www.hotelexpress.ru/ (in Russian, so if you won’t find the common language with it, tell me & I’ll try to help you)
http://www.sindbad.ru/hotels.php (tour company well known among students)

If you have any other questions, feel free to speak up! And I hope you’ll enjoy your visit to Russia—the biggest country in the world! :)