It is possible to get a visa based upon staying at a specific hotel, but then cancel the reservation after receiving the visa. I have done this several times during visits to Russia. You still will want to have the hotel you end up staying at register you though, or else you will have trouble exiting the country. When staying privately, we have made hotel reservations to get the visa invitation letter, then cancelled the hotel reservation, and stayed with a friend who did the registration procedure through the local city office. If your stay is short enough, 48 hours, I think, not counting weekends, you don't have to register.