last year, we stayed in a bunch of different accommodations. This was an independent trip (not work, not organized in any way)
From the Courtyard, Park Inn, some other local run hotels, and a private hostel, and another few nights on trains.
On exit, noone cared about registration.
The visa was date-specific for entry and exit, and they demanded flight bookings.
The consulate also demanded pre-paid hotel bookings since we used one of the invitation mills.
So stupid, since we just ended up booking cancellable reservations on Expedia, sent it into the consulate as "proof" and then cancelled the hotels.
Once in Russia, you can stay and go wherever you like, and dont have to use anything (cities visited/hotels) on your invitation letter, as long as you leave by the date on visa.