A UNESCO World Heritage Site, the 3-tiered Buddhist temple of Borobudur dates back to the eighth century and is one of the world’s great religious monuments. Watching the sun rise over the ancient carvings and the towering peak of Mt. Merapi is an experience not to be missed. Once you’ve explored the site itself—an adventure best enjoyed with a guide—consider joining a tour that includes a cycle trip through the timeless rice-field landscapes and unspoiled Javanese villages around Borobudur, perhaps with lunch at a farmer’s restaurant. History buffs will want to add the smaller nearby temples of Mendut and Pawon.

Travel back closer to the city to discover a second UNESCO World Heritage Site: the 10th-century Hindu temple complex known as Prambanan, with its towering spires and fragmented shrines. The site sprawls over many square miles and makes for a rewarding cycle adventure. Consider staying for the sunset and then watching the Ramayana Ballet. Performed on an open-air stage during the dry season and under cover during the wet, it’s a magical reenactment of ancient Hindu legend that draws on dance, drama, and music. Some packages include dinner while you watch, as well as round-trip transfers.

Spend the evening taking in Yogyakarta’s other sights—the sultan’s palace, royal tombs, the historic silversmithing district of Kota Gede, crumbling water gardens—as well as its vibrant modern-art and nightlife scene, whether by becak (cycle rickshaw), powered vehicle, or on foot. Alternatively, savor Yogyakarta specialties such as gudeg (jackfruit stew) or the bite-size morsels known as nasi kucing (banana leaf–wrapped rice) along Jalan Malioboro or on a street-food tour, and soak up the history as you explore the charming old town.