A tourist visa must be registered by a hotel. They do the "landlord" thing and registration all together. The new law applies to all of Russia but who knows if it's enforced in the villages. But if you get caught at the train stations without a registration life could become unpleasant. All this is a result of the recent terrorist bombings. In 2000 I too got a tourist visa via a Russian travel agent (the good old days! ) and stayed in a friend's flat. No problems. Just registered a few weeks down the line when we went touring and needed to stay in a hotel. Had to pay a $2 fine at the local police station (talk about cultural experiences!) but it was no big deal.
But in February after the metro bombing the police started checking everybody. I've heard of some foreigners having the cops escort them home to make sure they are really living in the flat they are registered at.
A tourist visa is only good for 30 days. They are no longer being extended. And if you stay over you could have difficulty getting a visa for your next trip. Again, what used to be a few dollars fine at the airport has turned into serious problems.