Kaliurang is a nature lover's paradise set amid high mountains in the wilds of Central Java. It's a small resort town built into the lower slopes of the active Mount Merapi volcano and comes with good walking and views.
Popular with local weekend visitors, Kaliurang's cool air and forested park trails are a good bet any time of year. There is a small fee to pay to enter the place, but it's well worth it. You can trek up Merapi Mountain by way of Kinahrejo village in the morning and return in the afternoon. When the weather is clear, the views from the mountain are breathtaking.
Be sure to check out Telogo Muncar while in Kaliurang. It's a pleasant waterfall with a nice plunge pool to swim in. Accommodation options in Kaliurang include many well appointed resorts as well as camping facilities.
Nearby Mount Plawangan is also worth a look if you have the time. The observatory here was moved to the town after the eruptions of the 1990s, but there are some WWII tunnels at the western flank to explore.
The gateway for Kaliurang is Adisucipto International Airport in nearby Yogyakarta, 25kms to the south. It's a busy little airport with flights from Jakarta (400kms to the northwest), and other Southeast Asian cities. It's less than an hour's flight from the capital. Local transport runs from Yogyakarta to Kaliurang via the Yogyakarta-Semarang highway.