Gongju National Museum is the essential indoor stop after the royal tombs. Its strongest galleries display objects excavated from King Muryeong's tomb: gold ornaments, swords, bronze mirrors, pottery, and the famous bronze shoes made for the afterlife rather than for walking.
The museum is not huge, but it gives Gongju its context. Without it, the tombs and fortress can feel like quiet archaeological sites; with it, the city starts to read as a former capital with links across Korea, China, and Japan.