The closest Russian point for all South American countries is Kaliningrad - when you face South America in that direction, Venezuela is obviously closer. (The closest Russian point for all North American answers, though, is eastern Siberia!)
I make the closest point in Russia to both countries to be Urup Island in the Kurile chain (I'm not counting the two islands further south that Russia and Japan are arguing about), and I make Nauru a whole 27 km / 17 miles closer than Kiribati.