A visa-free passenger may leave the ship for 3 nights, but he/she will have to present a paid hotel confirmation to a border guard. Then, during the hotel check-in, a hotel staff will register the guest with the appropriate authorities. These are pretty much all the conditions that have to be met if one wants to stay outside of a ship for 3 nights.
I don't know how the check-in process works for Russian Airbnb, but I think it can be used as a loophole to visit Moscow for one night without being discovered by the authorities. Last time I heard, Moscow police reduced their "random" spot checks on the streets and at subway stations (especially for white foreigners), so this should not be a problem either.