Yogyakarta

A 9th-century Buddhist monument whose lower galleries carry reliefs along the walls like a corridor. The daily number let onto the upper terraces is capped, so it needs booking, and you climb in sandals given out to spare the stone. No one goes up unguided.

The Shiva shrine at the centre stands tallest, ringed by a crowd of sharp-tipped towers. An earthquake in 2006 brought several down, and fitting the stones back together is still unfinished. On dry-season nights the Ramayana dance goes on the open-air stage.

The sultan still lives here, so only a few courts at the front are open to look at. It opens in the morning, then closes in the early afternoon, which puts it first in a day's plan. In the yard, court music and dance change with the day of the week.

An 18th-century water palace, with three bathing pools stepped one behind another inside the wall. A short walk off, an underground mosque sends five stairways up from a round room. Houses have filled the gaps between the ruins, so you find it by asking.

The street runs due north from the kraton, on the line that ties Merapi to the southern sea. Widening the pavement pushed the stalls into purpose-built sites, so you no longer eat off the road itself.

Jeeps cross the village ash buried in 2010. One house was kept as it stood, a museum where a clock and bowls sit melted out of shape. If the mountain stirs, the upper part shuts and the day's limit is set then. Ash blows, so start early in the morning.

A hilltop palace site looking down on Prambanan, where a double gateway and the footings are all that survives. The west is open, so a crowd builds for sunset and the ticket costs more at that hour.

Black sand facing the southern ocean, where the seabed falls away sharply and the surf drags people out. A story holds that the goddess of the south sea takes anyone in green, and people still avoid it. Horses and carts are hired by the hour on the sand.

Late in the afternoon only the cloth side still trades, so the food is a morning errand. The market closes off the southern end of Malioboro, the ground floor stacked with batik. Upstairs the smell turns to dried fish and spice, jamu ingredients behind.

This was the seat of the 16th-century Mataram kingdom, and silver workshops still fill its lanes. You can watch the hammering and soldering at the back of a workshop, and pieces are priced by weight.

A museum of Javanese culture beside the north alun-alun square, opened in 1935. It holds gamelan instruments, kris daggers, masks and wayang puppets. In the evening a wayang kulit show runs on a separate ticket.

The square south of the kraton, where walking blindfolded straight between its two banyan trees supposedly makes a wish come true. In the evening people rent pedal cars strung with lights to circle it. Stalls around the edge sell wedang ronde and grilled corn.

An 18th-century Dutch fort where Malioboro runs out to the south, today housing a museum of the independence struggle. Dioramas run through the barracks inside the moat and walls. Gedung Agung, the presidential palace, faces it across the road.

A Buddhist temple from the 9th century, about 3km east of Borobudur. Inside sits a 3m Buddha with both legs lowered, as if on a chair. Each year the Vesak procession sets off from here and walks to Borobudur.

Two identical main shrines stand side by side at this 9th-century Buddhist site a short way northeast of Prambanan. Tradition credits a Hindu king and his Buddhist queen with building it together. Far quieter than Prambanan, it fills with tripods at sunset.

A vertical sinkhole in Gunungkidul that you are lowered into by rope for tens of metres. Cross the forest floor into the next cave, and near midday a shaft of light falls through an opening above. With a daily cap on visitors, it needs booking.

You lie back in an inner tube and drift down a river running through a cave in Gunungkidul. Guides tie the tubes in a chain and tow them, torchlight picking out stalactites and bats overhead. When storms swell the river, trips can be called off.

A white pillar where the straight road north from the kraton ends. The original fell in an 1867 earthquake; the Dutch rebuilt it shorter. It sits on an imagined axis linking kraton and Merapi, and every evening the junction fills with photographers.

A hilltop burial ground for the sultans of Mataram, reached by several hundred stone steps. Entering the tombs means changing into Javanese dress lent at the gate, and they open only on set days. The village below the steps is the home of wedang uwuh.

A Hindu temple from around the 9th century, on the highest hill of any temple in Yogyakarta. The plains open out to the west, and at sunset you can watch planes coming down to land. Scooters labour on the steep climb up.

A Hindu temple found in 1966 when a farmer's hoe struck stone. Buried under Merapi ash, it still lies more than 6m below the surrounding fields, so you walk down steps to see it. It is near the old airport road yet gets few visitors.