If you want your Russian experience to be genuine, choosing homestay accommodation is the way to go. Agencies are increasingly offering various levels of homestay facilities to enable travelers to spend time living with Russian families.
Staying in a hotel might be more private and sometimes more comfortable, but it's usually more expensive, and who do you really meet - a couple of locals on the reception desk who are too busy for casual conversation. If you spend your nights with a Russian family, not only will you have a glimpse of everyday Russian life from the inside, you're also likely to learn plenty from them: handy tips for sightseeing in town, how to get around on the Metro system, or where to get the best coffee.
Agencies which organize homestays usually, of course, check that the facilities and sleeping arrangements in a homestay flat or house are suitable. You will always have a private room to sleep in, but usually share a bathroom with the family. Most packages include breakfast provided by the host; you can often pay extra to have Russian dinners, too. The host will often give you a key so you can come and go as you want. And you can often choose whether you'd like a host who speaks English, or want to brush up on your Russian.
Personally, I've had two trips to Russia and homestayed in a range of both cramped flats and stylish apartments in Irkutsk, Vladivostok, St Petersburg and Moscow. I've been hosted by an entire family with teenagers; often, middle-aged widows have been the ones making my tea for breakfast; and once in Moscow, the handsome son of a widow took over the duties when his mother was suddenly in hospital.
Staying with locals enhanced my time in Russia so much that sometimes my tales of fun with my hosts outshine my memories of Red Square or visiting the Hermitage. In Vladivostok, my host fascinated me with her take on socialism versus capitalism, putting my school textbook history into context. And a café recommendation from my St Petersburg host led me to the best Russian lunch ever.
Even if you're normally a hotel-lover, try a homestay just for part of your Russian trip. For me, seeing the country from the inside is the only way to go.