Senganen: You could easily spend the entire day at the summer home of the Shimazu family, with extensive formal gardens, views of the volcano, a traditional house, a museum, several restaurants and souvenir shops overflowing with quality handicrafts (8 miles north of the port).
Mount Sakurajima: You can take a 15-minute ferry ride to this 3,665-foot volcano, visit the Arimura Lava Observatory and explore the lava fields. In addition, there's a visitors center and free thermal foot bath a short walk from the ferry (6 miles north of the port).
Further afield: Outside of town, you'll find Chiran, a 250-year-old samurai village (22 miles south of the port) and Ibusuki, a resort town known for its natural hot springs (24 miles south of the port).
Museums: Culture buffs can visit the Kagoshima City Museum of Art, the Museum of the Meiji Restoration or the Reimeikan Museum, which focuses on the art of sword-making (all 4 to 6 miles north of the port).
Shochu Tastings: Producers might organize tastings at the pier, and shore excursions often hit one of the city's distilleries.