Yes, you can buy authentic Tanjore paintings directly in Thanjavur. Thanjavur is the birthplace of Tanjore painting. You can find numerous art galleries, studios, and shops in Thanjavur specializing in Tanjore paintings. Some notable places to purchase authentic Tanjore paintings include the Tanjore Art Gallery, located near the Brihadeeswarar Temple, and various art shops and studios scattered across the city.