I was in Busan last week. Don't speak any Korean but had a local friend to show me around. The police in the last month have done a major clampdown on restaurants/markets selling dog, and the places now are mostly hidden, although it might be more open in future if the police back off.

A few enquiries at restaurants previously famous for dog gave us hints where we could find it, and they were mostly small back-alley restaurants, initially denying they had dog, but happy to serve it once they gained our trust.

Don't really see the appeal myself, the meat isn't all that nice - I ate it more for the novelty factor.