I've visited Russia many times - mostly St. Petersburg.
Baltic Air/Swiss had a smoking deal: $470 round trip to Tallinn - no luggage included but $75 each way for luggage. From Tallinn, it is a 35 to 50 euro bus ride each way. The flight from SF was great: 1 stop and 15-16 hours elapsed. The bus ride and transfers add another 12 hours roughly. Not great but fine at that price.
To compare: Flights through IST or Dubai are $2000; $2500 to $3000 for economy during holiday season. Ouch! Even getting a miles ticket to IST - you still end up paying at least $800 for the round trip to/from Russia and likely will need to stay a night each way to get the timing right.

I tried to take advantage of the smoking deal: had everything ready to go but the visa was the issue.
Short summary: you normally need to get an invitation from a hotel if you are visiting as a tourist. This is quite simple - there are web sites to do this if you aren't actually staying at a hotel there.
Payment these days is challenging due to the Visa/MC cutoff, but the hotels now accept reservations with payment after you arrive.
In my case, I got the invitation and all the relevant docs. Some sort of health insurance is now required but no testing - the invitation service offered 1.8 euros/day health insurance which is dirt cheap. For everything else: bring cash. No problems trading dollars or euros for rubles in Russia but don't expect to get money via ATM or credit card or anything else remotely connected to Western financial systems.

However, the process of getting the visa itself was the problem. Even though I booked my ticket 12 business days before departure and inquired with visa companies 11 days before departure, not one single place would guarantee that I would get the visa in time.
This is apparently because nobody is allowed to do in-person visa applications anymore - not regular people nor professional services. Since everything must go by post - the Russian consulate is advising 3 weeks minimum(!) to get a visa while the services said 10 days but wouldn't guarantee it.
So I wound up cancelling Grrrrr.