This question really gets boring, or not ? Wikipedia had some updates trying to define the "real" border between Europe and Asia. But on this nice map you clearly see without any doubt, that at least Khevsureti, Tusheti and a small part of Khevi ;-) are parts of Europe.
Personally I think, that Georgia will very soon benefit from its strong geo-strategic position between Europe and Asia. I understand the wish for joining the EU very well, but I don't wish the Georgians all the over-regulations, the bureaucracy and the patronizing lately so characteristic for Europe. (Here is just a random link (German))
A FistfulofEuros today displays its Kaffeekranz-Discussion, don't miss the long section of Comments (most commenters had never been in Georgia or Armenia but clearly put the two to Europe but Azerbaijan to Asia...
Who had been in the Caucasus knows, it just belongs to heaven.
Ok, lets put it different: We're retagging Batumi to Europe and Friedrichshain to Asia.
Thanks to Registan.net