Hotels
These are again not up to Western standards in most cities, but in Moscow and Saint Petersburg they have 5 star Hotels. But you will pay a very high price to stay there. My suggestion would be to try to stay at a lower priced hotel and just don't expect a lot.
You can also do a ‘home stay’ by invitation from a Russian family, this is the best way to experience Russia. Many Russians advertise for them and there are numerous organizations that will make these arrangements for you. I suggest you pick up the book " Lets Go to Eastern Europe on a Budget". It is in most bookstores in the Travel Section. It is updated and published yearly. You can also try Youth Hostels as a cheap alternative.