The visa policy of Georgia has recently changed frequently and at the moment looks as follows:

The visa for visiting Georgia to Russian citizens is not required if the visit does not exceed 90 days, which is enough to indulge in domestic wine and "Borjom" to strengthen health. The only thing is that you will not be able to enter Georgia with marks in the passport of the border services of South Ossetia or Abkhazia, so it's better to visit these wonderful countries in the "reverse" order. By the way, if 3 months in Sakartvelo seem to you a little, your stay can easily be extended on the spot. No other registration is required for Russian citizens.

More details can be found on the page "Visa to Georgia."