The Art Newspaper reports that Russia and Gerogia are trading charges over war damage to cultural sites within Georgia and the break away region of South Ossetia. See: http://www.theartnewspaper.com/article.asp?id=16452
It seems churches and monasteries were hit especially hard. Presumably, this is due to the sheer number of such structures and the lack of many other targets of cultural significance. Apparently, there simply are more historic religious structures in the area than anything else given Christianity's long history in Georgia and the general lack of development in the border region.
Certainly, the damage that has been reported to cultural sites seems to be more of the collateral sort. There does not appear to be the sort of destruction directed at religious structures that occurred in the Balkans during the breakup of Yugoslavia. This probably should not be too surprising. Both the Russians and the Georgians are adherents to the Orthodox Christian faith.
In another move, the Georgian government has decided to convert an old museum in Gori dedicated to Stalin (who was born there) into a "museum of Russian aggression." Presumably, this move is yet another slap at Putin and the current Russian government. As noted elsewhere in today's New York Times, Russia has started to rehabilitate Stalin into a nationalist hero. See: http://www.nytimes.com/2008/11/27/world/europe/27archives.html?pagewanted=1&_r=1&ref=todayspaper ("Last year, the Kremlin promoted a study guide for high school teachers that deems Stalin “one of the most successful leaders of the U.S.S.R.,” while describing his “cruel exploitation” of the population. Mr. Putin himself has acknowledged the losses under Stalin, but has said Russians should not be made to feel ashamed of them.")