There is already information in this forum about Russian transit visas obtained in Tbilisi but nothing yet about tourist visas. Russian tourist visas are also quite easy to obtain in Tbilisi. I have a USA passport, so hopefully someone with another passport can add their experience to this thread as well.
Here's what I needed:
A photocopy of my passport
A tourist voucher (obtained online)
A completed application (filled out online after you receive the tourist voucher)
A passport photo
$180 USD (some embassies take credit cards, others only cash)
The tourist voucher was free from http://www.saint-petersburg.com/russian ... a-support/
, after booking a night in a hostel through their booking.com affiliate link (can be cancelled for free later).
You need the tourist voucher before filling out the application, but you'll receive it in just a few hours from when you request it. On the application, make your start date the first day of the hotel booking. USA citizens can receive 3 year visas, but the tourist voucher site will only give you a voucher for the days of your booking. The end date on the voucher doesn't matter, just make the exit date on your application 3 years after the entry date.
Here's my experience at the embassy:
I first had a Russian-speaking friend call the embassy to ask what I would need (actually, it's not an official embassy, but rather a Russian interests section of the Swiss embassy, which for visa purposes makes no difference). It turned out that one of the ambassadors speaks English so I talked to her. She told me that in order to receive a Russian visa with a USA passport, I need to bring a passport copy, tourist voucher, visa application, photo attached to the application, and $180 USD, any time during their opening hours. The USA and Russia have an agreement for 3-year tourist visas and she specifically added that I don’t need a hotel reservation for this visa, only a tourist voucher (effectively telling me that it’s totally ok to cancel my hotel reservation as soon as I receive the voucher).
I showed up to 53 Chavchavadze St in Tbilisi to find a big crowd standing outside, but walked right up to the guard at the entrance and he waved me in when he saw my American passport. One guy at the reception desk inside spoke English and told me to wait outside for 20 minutes. I went back outside, a bit confused. After 20 minutes, the security guard told me (in Russian) that I couldn’t take my backpack inside. I went to the supermarket next door and asked to leave it there, which was fine. The police gave me a slip with a number and I walked through the door with several others into a waiting room. When my number came up on the screen, I went to talk to the ambassador who told me that it would be no problem to give me a 3-year visa. I paid the cashier and she gave me a paper saying to come back in nine days.
Nine days later, I called the embassy in the morning and they told me to come at 2pm. This time the guard wouldn’t let me skip the crowd, but it turned out that everyone was there to pick up visas so the line moved very quickly. Half an hour later I had my passport with the visa inside.