The cost of living in Moscow is just about the same of in New-York says the last international cost of living survey...
I had found this address when I was planning on going. I had to cancel my trip before booking, but the comments in the Lonely Planet and the feeling from the emails we exchanged were very good. Not a hostel, but a private home, around 10 Euros a night (in 2004) and they provide the invitation letter (most hotels/hostels will though) : email@example.com
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»»»18 Euros and up
»»»On the site $40 is mentioned, but in LP $15+breakfast...