SOCHELNIK

As already has been said, the name of SOCHI if Kartvelian and means 'fir-tree'.

In the famous Russian dictionary of Vladimir Dahl there is an out-dated word "сочельник" (sochelnik) meaning  (Christmas) Eve. The official etymology connects it to the word "сочиво" (sochivo), some ancient dish eaten during Christmas. The etymology is questionnable for it clings at the root of 'sok' (juice), while the dish (kutia) is not very likely to be associated with juice.

But even if we agree that 'sochelnik' comes from 'sok' (juice), we still need to explain the name of today non-existing village of Sochely in Ivanovo region of Russia:

http://wikimapia.org/11330462/ru/Сочелы

You should agree that from 'sochelnik' it's much closer to 'sochely' than to 'sok'/'sochivo'. And the village's name is not likely to relate to juice either.

What is all this about? It's about tying 'sochelnik' to the Georgian word 'sochi' meaning 'fir-tree'. The tradition of putting a fir-tree on Christmas is well-known. Besides, 46% of the Ivanovo region are fir-tree forests, so it's full of fir-trees, and the name of the village is very likely to relate to that meaning too. And finally, the Georgian language has not only the noun 'sochi', but also its derivative adjective 'socheli', meaning not only 'of Sochi' (city), but also 'of fir-tree'.